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Page 1: (JJ - alas.matf.bg.ac.rs

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Page 2: (JJ - alas.matf.bg.ac.rs

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Page 3: (JJ - alas.matf.bg.ac.rs

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= N x) eP(Ii) = 0

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b ~ ~ b b be c ebb ~

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N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

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a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

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y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

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bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 4: (JJ - alas.matf.bg.ac.rs

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reg 21=M

C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j

c~ -~ rn lt~ -- t

)

iv- ~

f1 I

~ Vvtz-t t G

) J U-IQ

tt

J1Jh A r=A It k)

OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1

b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

nOUlJV o -iVV I 0 ~ A

~ 100 i11 1 1 0

~ i ~Iv - yYI

JA 2~b ~l=

l~c)J I

10 SAyoshy t~ b (0 ~i

J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )

-= - f5 - 2 )~~-

0 =tI f

~_O~L

m ~y-- (~l1J -J - ~ ~

(~3~A

) Y =c s h

-I ) (~ ([~~

~J)en_pound nOJ ~jlle C J

reg Gf~fr~ d~- J L1 (0 (1)

I t A

j )A (~)~ ~WC-~2~l)

I

1=M ~

b~-=~ U ~ ~ (A ~J I 1

1)(~

8f I) __

J ( lJ L(-I2 8 8raquo ~ 7

~I ~L

21 f t1shy

1 = c i

JI (Q~- 2_ lt-Gl VI v J

Q_ ~ -1 i) J 1 rebk hA i

JIJ ~ ) ~

CUC10 rP0e~-u---vj A

y - f l- L ~ =- rv b r3

J (111f)pound~)~ f1 I t1

)J =- ~l~ ~ VV _ L I

A

M hA _ _

IV_ tt

~~ ~ A A 3~ LA -== II 5- -4 f

olt0

I f- ~ c ~ ~ II

( 1-7 I

x =+ 1

C-Oj ~ j~ ~ - ~S

(NY

(25 j JshyM1 - ~ fAshy

~- G~

k ~--= (~ )~1 J = ~ 51 ~S-

j5K~ ~ ~ 8~ ~~ S - 3

I _

t

bJ v -= _~ ( shyf 5 ~ A )3- l

10 ~ ~S S~ ~

~~k L S c

I

( - G(~ (~ vr c 111

~-J 0~C -~I

S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V

I f Ii c

y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J

I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~

Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull

( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij

d J OJ

( r )

( J I ~~ ~ 0

ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~

c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J

v)J (~J J - (V U) ch

j-A J ~)d l)cJJ ia d

1(t cZ I j

_ i I

I ~Jlt+~ L1JJrl-h~ Ii i

i

(IA) ~--~ ~ 53 VI

) -lQn~crto-

)e GflJ~ ~~tt14 tt

( ~l ~~l ~ L ~l~ 1

~

r ftX

k~

(lV1fD- G fOI D --I

J

2oo~

t r(M bull ~) ~ ( ~) j If (~)

~CC ~) ~ ~(L~r =~~~~~

1 i) ( ~-

(~ (X)) A

~ (~GO A

1(00 I

~ 2shy

100 - 2

~ (V) ) V) ( i ~ ~J

CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc

13~ L Co

~J ~~ -5 _j -==

AJlj 2- ~~_tL1f 312shy k ~N~~j -

v I1-

---shy1

t9~J -- 1shy

cf y ( ~ i-J ~~

~(1-) (-~-1 ) ~ - ~t

3~2 - Lmiddot (

1 bull

)

- ljx S

L X I - --

I - jtv ty- ~ rfl 2 a lr1 -iJ

~-v~ ---~ - l r A

- (Ml -shy-

I f

~ k -tampJ -= LA t CG t reg

fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

d~c0

dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

-I 0

-t t) ) ~ 6--e~~~~ J~ oj

middot~middotLAi~V(

d

~ t t2~~ l)

~ =0 -tL bull

c ~ )--ti

l ( ()

C0Q]) IAVI jEth f ~

2d (3 L I I-t S) - ~

~ )

I 0

( ~ -1 ( )

reg L9A oj1 =-LO CA L C

u 1 ~ )

0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11

I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k

(JY61 i Jil~y 40

T -BQNlQ ~ 1J) ---J

ImiddotGS ~ 0

1 ~ --z11

0 -

~ B ) ~~ ~ ~ ) I A (

J J

j (J ~ky ~ -3 G

0~ ~ G ~~~t

J -= - V Z-~~) - t ( tc-1)

JJrOl(ff-1 v A~ 1 ~f1

nbull bull -= tCshyv VI_

W1 d

bltf L 1

-=r

(1~lmiddot1l-t- 4 L - =

-

- t

tmiddot

( I t

) J C ~

-y ygt 1 f

) ~j v ~

1-- i

ff

11

N2-d( I

I)]

~ ( 1

(1 - It) middot -- 1~to

I X 10 cO xV A - i

Jlfr~~06V ~f-knA

(j f~) f- j J e

J

( Y j J I ~- X fltj

I

I~ l

i V

f

i j l f

Y f 1 Z )l

~ll+r Ul)4~~f)~4-~~QC_~[Atil11

f ~ V

] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_

-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA

et~ pound~O~Amiddot M rfkip1middot MA- Tf1

amp0 ~ AvA -II middot0

Y~7 ~(() Xl=X

~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~

- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -

Jz ~ - ~

CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J

11 ~~Lr)1 j~ = )lt K J

~0 )iV Y Kj) ~

-

middotrv~(R) ~middot1

C c-C

11 -no rV-tv~e -D he))N~re

S~ p 2 I f i LK~- ~A CJ)064

lt VI 1 f

~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~

~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~

1 (1-) fT I6 b f ~ e) A-t___ I I _

s

IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU

~o r~ J11 flt

r)r

~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -

UiJ)i = f

lAY (( f ~) lw (A-) ~ j~lr C~)e

I tr ( tJ )) =IT (Ai V 111 (6)

r~ fh~

10u If) ~ T

1Ci lJ) ~ 1

Iv- (Q ) 1shy t

lt~ ~gt ~r- ~

-T (=7 T 1- ~gtl

Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd

(vI() p- f j~Pi

- Jli- (f) L= J-L

__i

l~ If~) ~ T

23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT

bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j

(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

rgt 1 bull (f~ ) ~() V (A I =_- ---

(p) 1shy

reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J

(1~ c no GCJ A PAaljrt tA~A 1 flczv A~

r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T

~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~

Jv C F) v Ir-( F( ~) ~ T

~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P

(lIJ tIt- (f) l Jf(fJ

lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~

t lID gt6 n-II~

X PtU () - I

( 1 t x B

- b( 1i f(i Imiddot l n i

r 1Y x (pYG) t C~ () c) I

it gt(~~ ~hC (t~ L )( C h n c

1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)

-iFt((~bC) (0dlCJ) b (~ nC)- --

PfC~ VJ tf1-) VlF0)

v r) ( [) ~ a r)_V --- I ok) ( P shyshy

1 plusmn T 1 T T ~

1- -j-T1shy I

IT 1 T T T T ~T) l 1-

T~I1 T T T L T T T)

1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy

-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l

- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-

L-JL-J --_---1

J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1

~ ) Cshy

_~ i1G f-CeVG ~c (A fJ)

J~ J~(- ~ ~

middotif ~ (J V f I

k

AQ~Jtt~ iA Jtf Je - i -

i

EE ihJ10~Q~-~X~ 1b~~~h~ ~~

ltJl

1~ b ~bU ( )) ~-=gt 1J ~ D 11

- ( fc (5 i

~ r

_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D

shy ~

fk

1 1

- L~-=-J-

L~0UC0 ~(~i

- - I

I) 1~1QJofL JA lt)

( Cv D) ~L

llt v ~ e fit ill

tr n

lJ

trU ~~) I

~~middotmiddotJ~~C6)- 1 bull

1~ A- J~)

t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)

A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj

JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A

t1 rf CF vl_ vr) (f J ~f) (

( AH0J)DtA L j j tk8HcrM AD HI

~ ft V f+l j V rt 11 I

blf J hUyjJ Pjf IJl L-1 1v CA)

-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~

lt2bJe ~ A-ltjTDJlOrlnj A

UVlU2ampO ft 15

M ~ t~JC~) bull p~~ cp (6)middot i i

~n(Orl~~ rsf~--Jb B~~ iI

0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j

I I i A~~rs r ~)~) iT~5~)~)

D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0

jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S

1 (Av rst~ liN ~~

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

-=It Fr ~ 1 r )

h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f

1 ~ rt-= 1+ ( I ~ t

-r~=

f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)

I I

i i i

l~l~~~~~ ~~ ~pMJI

I I I

(

-sJIt HlJ~

7 Iv- (PrJ) V Pn )

Fi L4-Cr) ~c r 7f 1(() - T

1 r ~ i Cf () ~Q

0K Hrp LA ~ n IIqtn r~ I hlf

v J

w ( ~ V jI

J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l

I -L i ti

l l-r T 1 l[ 1 ldJ 1 T [I

I

J r 1- T T j i- T i

I

I Tr I

I

T -- shy

J_ 1 11-I I

I I 1I

bull If V ~ (

Y1~ (f 0

~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)

~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)

~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )

-I -

TT -i 1 T

-I

r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

I _t _ shy

1 1 T T 1- 1shyT 1shyT iT T2- 1

i _I I

1 1 1 IJ- l- T

-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--

~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)

j (--1 f 1 ~l ~ l ()

reg

crJk)ttll tAUlll

i ~rl_

TVIHttmiddot~ H ~

~ TC~) ~)

X( G ~)J

~~ i

i16~i~(f)(L) ~

( tJ(~) ii

pF~~h) ~ F[PvfJI3) 1 (~) C~)

~o tiC f~(8) 11 rJ(p (1) J

h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

~ gtJ

6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ

~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl

I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z

i

=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 5: (JJ - alas.matf.bg.ac.rs

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9 ( ) Co I r- gt ) f l 0 n~- rth J rd b ) (-1 0 i

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C-Y(r~~ j ~

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C_ (i ri fdEJ lt r v

t l~ 0

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l

t~d

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shy shy ~ _i

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lrf fl r

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i-Ax-gshy

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

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GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

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bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

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bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

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a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

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y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

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bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

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bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 9: (JJ - alas.matf.bg.ac.rs

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eN = 1

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= N x) eP(Ii) = 0

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b ~ ~ b b be c ebb ~

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N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

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X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 10: (JJ - alas.matf.bg.ac.rs

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CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

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I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

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GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

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GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 11: (JJ - alas.matf.bg.ac.rs

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( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

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middotlaquo(~1 e) V1 R(Y-I e)

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~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 12: (JJ - alas.matf.bg.ac.rs

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C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j

c~ -~ rn lt~ -- t

)

iv- ~

f1 I

~ Vvtz-t t G

) J U-IQ

tt

J1Jh A r=A It k)

OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1

b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

nOUlJV o -iVV I 0 ~ A

~ 100 i11 1 1 0

~ i ~Iv - yYI

JA 2~b ~l=

l~c)J I

10 SAyoshy t~ b (0 ~i

J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )

-= - f5 - 2 )~~-

0 =tI f

~_O~L

m ~y-- (~l1J -J - ~ ~

(~3~A

) Y =c s h

-I ) (~ ([~~

~J)en_pound nOJ ~jlle C J

reg Gf~fr~ d~- J L1 (0 (1)

I t A

j )A (~)~ ~WC-~2~l)

I

1=M ~

b~-=~ U ~ ~ (A ~J I 1

1)(~

8f I) __

J ( lJ L(-I2 8 8raquo ~ 7

~I ~L

21 f t1shy

1 = c i

JI (Q~- 2_ lt-Gl VI v J

Q_ ~ -1 i) J 1 rebk hA i

JIJ ~ ) ~

CUC10 rP0e~-u---vj A

y - f l- L ~ =- rv b r3

J (111f)pound~)~ f1 I t1

)J =- ~l~ ~ VV _ L I

A

M hA _ _

IV_ tt

~~ ~ A A 3~ LA -== II 5- -4 f

olt0

I f- ~ c ~ ~ II

( 1-7 I

x =+ 1

C-Oj ~ j~ ~ - ~S

(NY

(25 j JshyM1 - ~ fAshy

~- G~

k ~--= (~ )~1 J = ~ 51 ~S-

j5K~ ~ ~ 8~ ~~ S - 3

I _

t

bJ v -= _~ ( shyf 5 ~ A )3- l

10 ~ ~S S~ ~

~~k L S c

I

( - G(~ (~ vr c 111

~-J 0~C -~I

S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V

I f Ii c

y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J

I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~

Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull

( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij

d J OJ

( r )

( J I ~~ ~ 0

ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~

c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J

v)J (~J J - (V U) ch

j-A J ~)d l)cJJ ia d

1(t cZ I j

_ i I

I ~Jlt+~ L1JJrl-h~ Ii i

i

(IA) ~--~ ~ 53 VI

) -lQn~crto-

)e GflJ~ ~~tt14 tt

( ~l ~~l ~ L ~l~ 1

~

r ftX

k~

(lV1fD- G fOI D --I

J

2oo~

t r(M bull ~) ~ ( ~) j If (~)

~CC ~) ~ ~(L~r =~~~~~

1 i) ( ~-

(~ (X)) A

~ (~GO A

1(00 I

~ 2shy

100 - 2

~ (V) ) V) ( i ~ ~J

CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc

13~ L Co

~J ~~ -5 _j -==

AJlj 2- ~~_tL1f 312shy k ~N~~j -

v I1-

---shy1

t9~J -- 1shy

cf y ( ~ i-J ~~

~(1-) (-~-1 ) ~ - ~t

3~2 - Lmiddot (

1 bull

)

- ljx S

L X I - --

I - jtv ty- ~ rfl 2 a lr1 -iJ

~-v~ ---~ - l r A

- (Ml -shy-

I f

~ k -tampJ -= LA t CG t reg

fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

d~c0

dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

-I 0

-t t) ) ~ 6--e~~~~ J~ oj

middot~middotLAi~V(

d

~ t t2~~ l)

~ =0 -tL bull

c ~ )--ti

l ( ()

C0Q]) IAVI jEth f ~

2d (3 L I I-t S) - ~

~ )

I 0

( ~ -1 ( )

reg L9A oj1 =-LO CA L C

u 1 ~ )

0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11

I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k

(JY61 i Jil~y 40

T -BQNlQ ~ 1J) ---J

ImiddotGS ~ 0

1 ~ --z11

0 -

~ B ) ~~ ~ ~ ) I A (

J J

j (J ~ky ~ -3 G

0~ ~ G ~~~t

J -= - V Z-~~) - t ( tc-1)

JJrOl(ff-1 v A~ 1 ~f1

nbull bull -= tCshyv VI_

W1 d

bltf L 1

-=r

(1~lmiddot1l-t- 4 L - =

-

- t

tmiddot

( I t

) J C ~

-y ygt 1 f

) ~j v ~

1-- i

ff

11

N2-d( I

I)]

~ ( 1

(1 - It) middot -- 1~to

I X 10 cO xV A - i

Jlfr~~06V ~f-knA

(j f~) f- j J e

J

( Y j J I ~- X fltj

I

I~ l

i V

f

i j l f

Y f 1 Z )l

~ll+r Ul)4~~f)~4-~~QC_~[Atil11

f ~ V

] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_

-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA

et~ pound~O~Amiddot M rfkip1middot MA- Tf1

amp0 ~ AvA -II middot0

Y~7 ~(() Xl=X

~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~

- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -

Jz ~ - ~

CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J

11 ~~Lr)1 j~ = )lt K J

~0 )iV Y Kj) ~

-

middotrv~(R) ~middot1

C c-C

11 -no rV-tv~e -D he))N~re

S~ p 2 I f i LK~- ~A CJ)064

lt VI 1 f

~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~

~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~

1 (1-) fT I6 b f ~ e) A-t___ I I _

s

IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU

~o r~ J11 flt

r)r

~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -

UiJ)i = f

lAY (( f ~) lw (A-) ~ j~lr C~)e

I tr ( tJ )) =IT (Ai V 111 (6)

r~ fh~

10u If) ~ T

1Ci lJ) ~ 1

Iv- (Q ) 1shy t

lt~ ~gt ~r- ~

-T (=7 T 1- ~gtl

Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd

(vI() p- f j~Pi

- Jli- (f) L= J-L

__i

l~ If~) ~ T

23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT

bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j

(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

rgt 1 bull (f~ ) ~() V (A I =_- ---

(p) 1shy

reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J

(1~ c no GCJ A PAaljrt tA~A 1 flczv A~

r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T

~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~

Jv C F) v Ir-( F( ~) ~ T

~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P

(lIJ tIt- (f) l Jf(fJ

lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~

t lID gt6 n-II~

X PtU () - I

( 1 t x B

- b( 1i f(i Imiddot l n i

r 1Y x (pYG) t C~ () c) I

it gt(~~ ~hC (t~ L )( C h n c

1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)

-iFt((~bC) (0dlCJ) b (~ nC)- --

PfC~ VJ tf1-) VlF0)

v r) ( [) ~ a r)_V --- I ok) ( P shyshy

1 plusmn T 1 T T ~

1- -j-T1shy I

IT 1 T T T T ~T) l 1-

T~I1 T T T L T T T)

1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy

-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l

- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-

L-JL-J --_---1

J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1

~ ) Cshy

_~ i1G f-CeVG ~c (A fJ)

J~ J~(- ~ ~

middotif ~ (J V f I

k

AQ~Jtt~ iA Jtf Je - i -

i

EE ihJ10~Q~-~X~ 1b~~~h~ ~~

ltJl

1~ b ~bU ( )) ~-=gt 1J ~ D 11

- ( fc (5 i

~ r

_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D

shy ~

fk

1 1

- L~-=-J-

L~0UC0 ~(~i

- - I

I) 1~1QJofL JA lt)

( Cv D) ~L

llt v ~ e fit ill

tr n

lJ

trU ~~) I

~~middotmiddotJ~~C6)- 1 bull

1~ A- J~)

t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)

A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj

JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A

t1 rf CF vl_ vr) (f J ~f) (

( AH0J)DtA L j j tk8HcrM AD HI

~ ft V f+l j V rt 11 I

blf J hUyjJ Pjf IJl L-1 1v CA)

-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~

lt2bJe ~ A-ltjTDJlOrlnj A

UVlU2ampO ft 15

M ~ t~JC~) bull p~~ cp (6)middot i i

~n(Orl~~ rsf~--Jb B~~ iI

0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j

I I i A~~rs r ~)~) iT~5~)~)

D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0

jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S

1 (Av rst~ liN ~~

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

-=It Fr ~ 1 r )

h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f

1 ~ rt-= 1+ ( I ~ t

-r~=

f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)

I I

i i i

l~l~~~~~ ~~ ~pMJI

I I I

(

-sJIt HlJ~

7 Iv- (PrJ) V Pn )

Fi L4-Cr) ~c r 7f 1(() - T

1 r ~ i Cf () ~Q

0K Hrp LA ~ n IIqtn r~ I hlf

v J

w ( ~ V jI

J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l

I -L i ti

l l-r T 1 l[ 1 ldJ 1 T [I

I

J r 1- T T j i- T i

I

I Tr I

I

T -- shy

J_ 1 11-I I

I I 1I

bull If V ~ (

Y1~ (f 0

~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)

~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)

~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )

-I -

TT -i 1 T

-I

r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

I _t _ shy

1 1 T T 1- 1shyT 1shyT iT T2- 1

i _I I

1 1 1 IJ- l- T

-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--

~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)

j (--1 f 1 ~l ~ l ()

reg

crJk)ttll tAUlll

i ~rl_

TVIHttmiddot~ H ~

~ TC~) ~)

X( G ~)J

~~ i

i16~i~(f)(L) ~

( tJ(~) ii

pF~~h) ~ F[PvfJI3) 1 (~) C~)

~o tiC f~(8) 11 rJ(p (1) J

h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

~ gtJ

6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ

~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl

I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z

i

=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 13: (JJ - alas.matf.bg.ac.rs

c -t E- ( t r- f)~ y ( (11 )J t - ( (JJ)

~E ((0J

X G- f- Ii )lt c D ~ C ~ -1 e D J

lf)j)E A-x( (~j) amp- GxCgt

t PyL

t- (-ty Craquo (

l L

i I 0~)~ ) y )-7shy

t ~ lY~)

Clt - l t Cmiddot

I Ii_ bull-lt F V tI 1 Ii (I )

V Y ( ( I~ c i~-4 J- (-b

l~- t ~) y J

imiddotJ

f lQ)

~ I

1 ( ~ laquo~J V J J J

1 t J

OC06

~

0 7I r c) JGlt lmiddot -r

) )

r) gt ( - --~

)

shy

(

(

~ilt Z - LA

-) J I( j ( -

~i- _y~~f~ ~j~ ~ ~ A~~A

~~ (~ ls) Ci_fshy~~~J- t]~(t)~~

r--c- f ~ ~~

- - - ~-- bull -shy

Cflt(V ~([~e~~- f K JO-~

V

-Ij--XtAshy

))_ jtt_~ _~~

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Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d

111-1

C -~d

S~ --+ ) 9A ~S--==0

CL = Me O-KZo M la-tr

CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J

bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

1= ~ 3 c

1~ --A~

reg 21=M

C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j

c~ -~ rn lt~ -- t

)

iv- ~

f1 I

~ Vvtz-t t G

) J U-IQ

tt

J1Jh A r=A It k)

OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1

b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

nOUlJV o -iVV I 0 ~ A

~ 100 i11 1 1 0

~ i ~Iv - yYI

JA 2~b ~l=

l~c)J I

10 SAyoshy t~ b (0 ~i

J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )

-= - f5 - 2 )~~-

0 =tI f

~_O~L

m ~y-- (~l1J -J - ~ ~

(~3~A

) Y =c s h

-I ) (~ ([~~

~J)en_pound nOJ ~jlle C J

reg Gf~fr~ d~- J L1 (0 (1)

I t A

j )A (~)~ ~WC-~2~l)

I

1=M ~

b~-=~ U ~ ~ (A ~J I 1

1)(~

8f I) __

J ( lJ L(-I2 8 8raquo ~ 7

~I ~L

21 f t1shy

1 = c i

JI (Q~- 2_ lt-Gl VI v J

Q_ ~ -1 i) J 1 rebk hA i

JIJ ~ ) ~

CUC10 rP0e~-u---vj A

y - f l- L ~ =- rv b r3

J (111f)pound~)~ f1 I t1

)J =- ~l~ ~ VV _ L I

A

M hA _ _

IV_ tt

~~ ~ A A 3~ LA -== II 5- -4 f

olt0

I f- ~ c ~ ~ II

( 1-7 I

x =+ 1

C-Oj ~ j~ ~ - ~S

(NY

(25 j JshyM1 - ~ fAshy

~- G~

k ~--= (~ )~1 J = ~ 51 ~S-

j5K~ ~ ~ 8~ ~~ S - 3

I _

t

bJ v -= _~ ( shyf 5 ~ A )3- l

10 ~ ~S S~ ~

~~k L S c

I

( - G(~ (~ vr c 111

~-J 0~C -~I

S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V

I f Ii c

y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J

I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~

Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull

( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij

d J OJ

( r )

( J I ~~ ~ 0

ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~

c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J

v)J (~J J - (V U) ch

j-A J ~)d l)cJJ ia d

1(t cZ I j

_ i I

I ~Jlt+~ L1JJrl-h~ Ii i

i

(IA) ~--~ ~ 53 VI

) -lQn~crto-

)e GflJ~ ~~tt14 tt

( ~l ~~l ~ L ~l~ 1

~

r ftX

k~

(lV1fD- G fOI D --I

J

2oo~

t r(M bull ~) ~ ( ~) j If (~)

~CC ~) ~ ~(L~r =~~~~~

1 i) ( ~-

(~ (X)) A

~ (~GO A

1(00 I

~ 2shy

100 - 2

~ (V) ) V) ( i ~ ~J

CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc

13~ L Co

~J ~~ -5 _j -==

AJlj 2- ~~_tL1f 312shy k ~N~~j -

v I1-

---shy1

t9~J -- 1shy

cf y ( ~ i-J ~~

~(1-) (-~-1 ) ~ - ~t

3~2 - Lmiddot (

1 bull

)

- ljx S

L X I - --

I - jtv ty- ~ rfl 2 a lr1 -iJ

~-v~ ---~ - l r A

- (Ml -shy-

I f

~ k -tampJ -= LA t CG t reg

fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

d~c0

dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

-I 0

-t t) ) ~ 6--e~~~~ J~ oj

middot~middotLAi~V(

d

~ t t2~~ l)

~ =0 -tL bull

c ~ )--ti

l ( ()

C0Q]) IAVI jEth f ~

2d (3 L I I-t S) - ~

~ )

I 0

( ~ -1 ( )

reg L9A oj1 =-LO CA L C

u 1 ~ )

0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11

I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k

(JY61 i Jil~y 40

T -BQNlQ ~ 1J) ---J

ImiddotGS ~ 0

1 ~ --z11

0 -

~ B ) ~~ ~ ~ ) I A (

J J

j (J ~ky ~ -3 G

0~ ~ G ~~~t

J -= - V Z-~~) - t ( tc-1)

JJrOl(ff-1 v A~ 1 ~f1

nbull bull -= tCshyv VI_

W1 d

bltf L 1

-=r

(1~lmiddot1l-t- 4 L - =

-

- t

tmiddot

( I t

) J C ~

-y ygt 1 f

) ~j v ~

1-- i

ff

11

N2-d( I

I)]

~ ( 1

(1 - It) middot -- 1~to

I X 10 cO xV A - i

Jlfr~~06V ~f-knA

(j f~) f- j J e

J

( Y j J I ~- X fltj

I

I~ l

i V

f

i j l f

Y f 1 Z )l

~ll+r Ul)4~~f)~4-~~QC_~[Atil11

f ~ V

] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_

-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA

et~ pound~O~Amiddot M rfkip1middot MA- Tf1

amp0 ~ AvA -II middot0

Y~7 ~(() Xl=X

~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~

- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -

Jz ~ - ~

CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J

11 ~~Lr)1 j~ = )lt K J

~0 )iV Y Kj) ~

-

middotrv~(R) ~middot1

C c-C

11 -no rV-tv~e -D he))N~re

S~ p 2 I f i LK~- ~A CJ)064

lt VI 1 f

~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~

~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~

1 (1-) fT I6 b f ~ e) A-t___ I I _

s

IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU

~o r~ J11 flt

r)r

~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -

UiJ)i = f

lAY (( f ~) lw (A-) ~ j~lr C~)e

I tr ( tJ )) =IT (Ai V 111 (6)

r~ fh~

10u If) ~ T

1Ci lJ) ~ 1

Iv- (Q ) 1shy t

lt~ ~gt ~r- ~

-T (=7 T 1- ~gtl

Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd

(vI() p- f j~Pi

- Jli- (f) L= J-L

__i

l~ If~) ~ T

23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT

bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j

(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

rgt 1 bull (f~ ) ~() V (A I =_- ---

(p) 1shy

reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J

(1~ c no GCJ A PAaljrt tA~A 1 flczv A~

r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T

~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~

Jv C F) v Ir-( F( ~) ~ T

~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P

(lIJ tIt- (f) l Jf(fJ

lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~

t lID gt6 n-II~

X PtU () - I

( 1 t x B

- b( 1i f(i Imiddot l n i

r 1Y x (pYG) t C~ () c) I

it gt(~~ ~hC (t~ L )( C h n c

1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)

-iFt((~bC) (0dlCJ) b (~ nC)- --

PfC~ VJ tf1-) VlF0)

v r) ( [) ~ a r)_V --- I ok) ( P shyshy

1 plusmn T 1 T T ~

1- -j-T1shy I

IT 1 T T T T ~T) l 1-

T~I1 T T T L T T T)

1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy

-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l

- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-

L-JL-J --_---1

J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1

~ ) Cshy

_~ i1G f-CeVG ~c (A fJ)

J~ J~(- ~ ~

middotif ~ (J V f I

k

AQ~Jtt~ iA Jtf Je - i -

i

EE ihJ10~Q~-~X~ 1b~~~h~ ~~

ltJl

1~ b ~bU ( )) ~-=gt 1J ~ D 11

- ( fc (5 i

~ r

_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D

shy ~

fk

1 1

- L~-=-J-

L~0UC0 ~(~i

- - I

I) 1~1QJofL JA lt)

( Cv D) ~L

llt v ~ e fit ill

tr n

lJ

trU ~~) I

~~middotmiddotJ~~C6)- 1 bull

1~ A- J~)

t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)

A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj

JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A

t1 rf CF vl_ vr) (f J ~f) (

( AH0J)DtA L j j tk8HcrM AD HI

~ ft V f+l j V rt 11 I

blf J hUyjJ Pjf IJl L-1 1v CA)

-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~

lt2bJe ~ A-ltjTDJlOrlnj A

UVlU2ampO ft 15

M ~ t~JC~) bull p~~ cp (6)middot i i

~n(Orl~~ rsf~--Jb B~~ iI

0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j

I I i A~~rs r ~)~) iT~5~)~)

D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0

jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S

1 (Av rst~ liN ~~

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

-=It Fr ~ 1 r )

h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f

1 ~ rt-= 1+ ( I ~ t

-r~=

f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)

I I

i i i

l~l~~~~~ ~~ ~pMJI

I I I

(

-sJIt HlJ~

7 Iv- (PrJ) V Pn )

Fi L4-Cr) ~c r 7f 1(() - T

1 r ~ i Cf () ~Q

0K Hrp LA ~ n IIqtn r~ I hlf

v J

w ( ~ V jI

J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l

I -L i ti

l l-r T 1 l[ 1 ldJ 1 T [I

I

J r 1- T T j i- T i

I

I Tr I

I

T -- shy

J_ 1 11-I I

I I 1I

bull If V ~ (

Y1~ (f 0

~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)

~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)

~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )

-I -

TT -i 1 T

-I

r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

I _t _ shy

1 1 T T 1- 1shyT 1shyT iT T2- 1

i _I I

1 1 1 IJ- l- T

-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--

~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)

j (--1 f 1 ~l ~ l ()

reg

crJk)ttll tAUlll

i ~rl_

TVIHttmiddot~ H ~

~ TC~) ~)

X( G ~)J

~~ i

i16~i~(f)(L) ~

( tJ(~) ii

pF~~h) ~ F[PvfJI3) 1 (~) C~)

~o tiC f~(8) 11 rJ(p (1) J

h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

~ gtJ

6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ

~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl

I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z

i

=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 14: (JJ - alas.matf.bg.ac.rs

1 ( ~ laquo~J V J J J

1 t J

OC06

~

0 7I r c) JGlt lmiddot -r

) )

r) gt ( - --~

)

shy

(

(

~ilt Z - LA

-) J I( j ( -

~i- _y~~f~ ~j~ ~ ~ A~~A

~~ (~ ls) Ci_fshy~~~J- t]~(t)~~

r--c- f ~ ~~

- - - ~-- bull -shy

Cflt(V ~([~e~~- f K JO-~

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fA~ ~ Lj = ~ t 1- r-dj I X I J e i-

Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d

111-1

C -~d

S~ --+ ) 9A ~S--==0

CL = Me O-KZo M la-tr

CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J

bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

1= ~ 3 c

1~ --A~

reg 21=M

C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j

c~ -~ rn lt~ -- t

)

iv- ~

f1 I

~ Vvtz-t t G

) J U-IQ

tt

J1Jh A r=A It k)

OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1

b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

nOUlJV o -iVV I 0 ~ A

~ 100 i11 1 1 0

~ i ~Iv - yYI

JA 2~b ~l=

l~c)J I

10 SAyoshy t~ b (0 ~i

J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )

-= - f5 - 2 )~~-

0 =tI f

~_O~L

m ~y-- (~l1J -J - ~ ~

(~3~A

) Y =c s h

-I ) (~ ([~~

~J)en_pound nOJ ~jlle C J

reg Gf~fr~ d~- J L1 (0 (1)

I t A

j )A (~)~ ~WC-~2~l)

I

1=M ~

b~-=~ U ~ ~ (A ~J I 1

1)(~

8f I) __

J ( lJ L(-I2 8 8raquo ~ 7

~I ~L

21 f t1shy

1 = c i

JI (Q~- 2_ lt-Gl VI v J

Q_ ~ -1 i) J 1 rebk hA i

JIJ ~ ) ~

CUC10 rP0e~-u---vj A

y - f l- L ~ =- rv b r3

J (111f)pound~)~ f1 I t1

)J =- ~l~ ~ VV _ L I

A

M hA _ _

IV_ tt

~~ ~ A A 3~ LA -== II 5- -4 f

olt0

I f- ~ c ~ ~ II

( 1-7 I

x =+ 1

C-Oj ~ j~ ~ - ~S

(NY

(25 j JshyM1 - ~ fAshy

~- G~

k ~--= (~ )~1 J = ~ 51 ~S-

j5K~ ~ ~ 8~ ~~ S - 3

I _

t

bJ v -= _~ ( shyf 5 ~ A )3- l

10 ~ ~S S~ ~

~~k L S c

I

( - G(~ (~ vr c 111

~-J 0~C -~I

S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V

I f Ii c

y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J

I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~

Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull

( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij

d J OJ

( r )

( J I ~~ ~ 0

ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~

c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J

v)J (~J J - (V U) ch

j-A J ~)d l)cJJ ia d

1(t cZ I j

_ i I

I ~Jlt+~ L1JJrl-h~ Ii i

i

(IA) ~--~ ~ 53 VI

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)e GflJ~ ~~tt14 tt

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~

r ftX

k~

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J

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t r(M bull ~) ~ ( ~) j If (~)

~CC ~) ~ ~(L~r =~~~~~

1 i) ( ~-

(~ (X)) A

~ (~GO A

1(00 I

~ 2shy

100 - 2

~ (V) ) V) ( i ~ ~J

CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc

13~ L Co

~J ~~ -5 _j -==

AJlj 2- ~~_tL1f 312shy k ~N~~j -

v I1-

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cf y ( ~ i-J ~~

~(1-) (-~-1 ) ~ - ~t

3~2 - Lmiddot (

1 bull

)

- ljx S

L X I - --

I - jtv ty- ~ rfl 2 a lr1 -iJ

~-v~ ---~ - l r A

- (Ml -shy-

I f

~ k -tampJ -= LA t CG t reg

fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

d~c0

dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

-I 0

-t t) ) ~ 6--e~~~~ J~ oj

middot~middotLAi~V(

d

~ t t2~~ l)

~ =0 -tL bull

c ~ )--ti

l ( ()

C0Q]) IAVI jEth f ~

2d (3 L I I-t S) - ~

~ )

I 0

( ~ -1 ( )

reg L9A oj1 =-LO CA L C

u 1 ~ )

0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11

I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k

(JY61 i Jil~y 40

T -BQNlQ ~ 1J) ---J

ImiddotGS ~ 0

1 ~ --z11

0 -

~ B ) ~~ ~ ~ ) I A (

J J

j (J ~ky ~ -3 G

0~ ~ G ~~~t

J -= - V Z-~~) - t ( tc-1)

JJrOl(ff-1 v A~ 1 ~f1

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W1 d

bltf L 1

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(1~lmiddot1l-t- 4 L - =

-

- t

tmiddot

( I t

) J C ~

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ff

11

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J

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I

I~ l

i V

f

i j l f

Y f 1 Z )l

~ll+r Ul)4~~f)~4-~~QC_~[Atil11

f ~ V

] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_

-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA

et~ pound~O~Amiddot M rfkip1middot MA- Tf1

amp0 ~ AvA -II middot0

Y~7 ~(() Xl=X

~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~

- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -

Jz ~ - ~

CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J

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middotrv~(R) ~middot1

C c-C

11 -no rV-tv~e -D he))N~re

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lt VI 1 f

~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~

~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~

1 (1-) fT I6 b f ~ e) A-t___ I I _

s

IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU

~o r~ J11 flt

r)r

~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -

UiJ)i = f

lAY (( f ~) lw (A-) ~ j~lr C~)e

I tr ( tJ )) =IT (Ai V 111 (6)

r~ fh~

10u If) ~ T

1Ci lJ) ~ 1

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Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd

(vI() p- f j~Pi

- Jli- (f) L= J-L

__i

l~ If~) ~ T

23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT

bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j

(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

rgt 1 bull (f~ ) ~() V (A I =_- ---

(p) 1shy

reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J

(1~ c no GCJ A PAaljrt tA~A 1 flczv A~

r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T

~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~

Jv C F) v Ir-( F( ~) ~ T

~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P

(lIJ tIt- (f) l Jf(fJ

lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~

t lID gt6 n-II~

X PtU () - I

( 1 t x B

- b( 1i f(i Imiddot l n i

r 1Y x (pYG) t C~ () c) I

it gt(~~ ~hC (t~ L )( C h n c

1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)

-iFt((~bC) (0dlCJ) b (~ nC)- --

PfC~ VJ tf1-) VlF0)

v r) ( [) ~ a r)_V --- I ok) ( P shyshy

1 plusmn T 1 T T ~

1- -j-T1shy I

IT 1 T T T T ~T) l 1-

T~I1 T T T L T T T)

1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy

-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l

- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-

L-JL-J --_---1

J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1

~ ) Cshy

_~ i1G f-CeVG ~c (A fJ)

J~ J~(- ~ ~

middotif ~ (J V f I

k

AQ~Jtt~ iA Jtf Je - i -

i

EE ihJ10~Q~-~X~ 1b~~~h~ ~~

ltJl

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shy ~

fk

1 1

- L~-=-J-

L~0UC0 ~(~i

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I) 1~1QJofL JA lt)

( Cv D) ~L

llt v ~ e fit ill

tr n

lJ

trU ~~) I

~~middotmiddotJ~~C6)- 1 bull

1~ A- J~)

t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)

A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj

JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A

t1 rf CF vl_ vr) (f J ~f) (

( AH0J)DtA L j j tk8HcrM AD HI

~ ft V f+l j V rt 11 I

blf J hUyjJ Pjf IJl L-1 1v CA)

-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~

lt2bJe ~ A-ltjTDJlOrlnj A

UVlU2ampO ft 15

M ~ t~JC~) bull p~~ cp (6)middot i i

~n(Orl~~ rsf~--Jb B~~ iI

0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j

I I i A~~rs r ~)~) iT~5~)~)

D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0

jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S

1 (Av rst~ liN ~~

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

-=It Fr ~ 1 r )

h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f

1 ~ rt-= 1+ ( I ~ t

-r~=

f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)

I I

i i i

l~l~~~~~ ~~ ~pMJI

I I I

(

-sJIt HlJ~

7 Iv- (PrJ) V Pn )

Fi L4-Cr) ~c r 7f 1(() - T

1 r ~ i Cf () ~Q

0K Hrp LA ~ n IIqtn r~ I hlf

v J

w ( ~ V jI

J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l

I -L i ti

l l-r T 1 l[ 1 ldJ 1 T [I

I

J r 1- T T j i- T i

I

I Tr I

I

T -- shy

J_ 1 11-I I

I I 1I

bull If V ~ (

Y1~ (f 0

~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)

~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)

~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )

-I -

TT -i 1 T

-I

r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

I _t _ shy

1 1 T T 1- 1shyT 1shyT iT T2- 1

i _I I

1 1 1 IJ- l- T

-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--

~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)

j (--1 f 1 ~l ~ l ()

reg

crJk)ttll tAUlll

i ~rl_

TVIHttmiddot~ H ~

~ TC~) ~)

X( G ~)J

~~ i

i16~i~(f)(L) ~

( tJ(~) ii

pF~~h) ~ F[PvfJI3) 1 (~) C~)

~o tiC f~(8) 11 rJ(p (1) J

h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

~ gtJ

6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ

~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl

I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z

i

=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 15: (JJ - alas.matf.bg.ac.rs

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V

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shy

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S~ --+ ) 9A ~S--==0

CL = Me O-KZo M la-tr

CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J

bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

1= ~ 3 c

1~ --A~

reg 21=M

C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j

c~ -~ rn lt~ -- t

)

iv- ~

f1 I

~ Vvtz-t t G

) J U-IQ

tt

J1Jh A r=A It k)

OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1

b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

nOUlJV o -iVV I 0 ~ A

~ 100 i11 1 1 0

~ i ~Iv - yYI

JA 2~b ~l=

l~c)J I

10 SAyoshy t~ b (0 ~i

J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )

-= - f5 - 2 )~~-

0 =tI f

~_O~L

m ~y-- (~l1J -J - ~ ~

(~3~A

) Y =c s h

-I ) (~ ([~~

~J)en_pound nOJ ~jlle C J

reg Gf~fr~ d~- J L1 (0 (1)

I t A

j )A (~)~ ~WC-~2~l)

I

1=M ~

b~-=~ U ~ ~ (A ~J I 1

1)(~

8f I) __

J ( lJ L(-I2 8 8raquo ~ 7

~I ~L

21 f t1shy

1 = c i

JI (Q~- 2_ lt-Gl VI v J

Q_ ~ -1 i) J 1 rebk hA i

JIJ ~ ) ~

CUC10 rP0e~-u---vj A

y - f l- L ~ =- rv b r3

J (111f)pound~)~ f1 I t1

)J =- ~l~ ~ VV _ L I

A

M hA _ _

IV_ tt

~~ ~ A A 3~ LA -== II 5- -4 f

olt0

I f- ~ c ~ ~ II

( 1-7 I

x =+ 1

C-Oj ~ j~ ~ - ~S

(NY

(25 j JshyM1 - ~ fAshy

~- G~

k ~--= (~ )~1 J = ~ 51 ~S-

j5K~ ~ ~ 8~ ~~ S - 3

I _

t

bJ v -= _~ ( shyf 5 ~ A )3- l

10 ~ ~S S~ ~

~~k L S c

I

( - G(~ (~ vr c 111

~-J 0~C -~I

S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V

I f Ii c

y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J

I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~

Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull

( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij

d J OJ

( r )

( J I ~~ ~ 0

ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~

c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J

v)J (~J J - (V U) ch

j-A J ~)d l)cJJ ia d

1(t cZ I j

_ i I

I ~Jlt+~ L1JJrl-h~ Ii i

i

(IA) ~--~ ~ 53 VI

) -lQn~crto-

)e GflJ~ ~~tt14 tt

( ~l ~~l ~ L ~l~ 1

~

r ftX

k~

(lV1fD- G fOI D --I

J

2oo~

t r(M bull ~) ~ ( ~) j If (~)

~CC ~) ~ ~(L~r =~~~~~

1 i) ( ~-

(~ (X)) A

~ (~GO A

1(00 I

~ 2shy

100 - 2

~ (V) ) V) ( i ~ ~J

CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc

13~ L Co

~J ~~ -5 _j -==

AJlj 2- ~~_tL1f 312shy k ~N~~j -

v I1-

---shy1

t9~J -- 1shy

cf y ( ~ i-J ~~

~(1-) (-~-1 ) ~ - ~t

3~2 - Lmiddot (

1 bull

)

- ljx S

L X I - --

I - jtv ty- ~ rfl 2 a lr1 -iJ

~-v~ ---~ - l r A

- (Ml -shy-

I f

~ k -tampJ -= LA t CG t reg

fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

d~c0

dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

-I 0

-t t) ) ~ 6--e~~~~ J~ oj

middot~middotLAi~V(

d

~ t t2~~ l)

~ =0 -tL bull

c ~ )--ti

l ( ()

C0Q]) IAVI jEth f ~

2d (3 L I I-t S) - ~

~ )

I 0

( ~ -1 ( )

reg L9A oj1 =-LO CA L C

u 1 ~ )

0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11

I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k

(JY61 i Jil~y 40

T -BQNlQ ~ 1J) ---J

ImiddotGS ~ 0

1 ~ --z11

0 -

~ B ) ~~ ~ ~ ) I A (

J J

j (J ~ky ~ -3 G

0~ ~ G ~~~t

J -= - V Z-~~) - t ( tc-1)

JJrOl(ff-1 v A~ 1 ~f1

nbull bull -= tCshyv VI_

W1 d

bltf L 1

-=r

(1~lmiddot1l-t- 4 L - =

-

- t

tmiddot

( I t

) J C ~

-y ygt 1 f

) ~j v ~

1-- i

ff

11

N2-d( I

I)]

~ ( 1

(1 - It) middot -- 1~to

I X 10 cO xV A - i

Jlfr~~06V ~f-knA

(j f~) f- j J e

J

( Y j J I ~- X fltj

I

I~ l

i V

f

i j l f

Y f 1 Z )l

~ll+r Ul)4~~f)~4-~~QC_~[Atil11

f ~ V

] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_

-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA

et~ pound~O~Amiddot M rfkip1middot MA- Tf1

amp0 ~ AvA -II middot0

Y~7 ~(() Xl=X

~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~

- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -

Jz ~ - ~

CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J

11 ~~Lr)1 j~ = )lt K J

~0 )iV Y Kj) ~

-

middotrv~(R) ~middot1

C c-C

11 -no rV-tv~e -D he))N~re

S~ p 2 I f i LK~- ~A CJ)064

lt VI 1 f

~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~

~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~

1 (1-) fT I6 b f ~ e) A-t___ I I _

s

IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU

~o r~ J11 flt

r)r

~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -

UiJ)i = f

lAY (( f ~) lw (A-) ~ j~lr C~)e

I tr ( tJ )) =IT (Ai V 111 (6)

r~ fh~

10u If) ~ T

1Ci lJ) ~ 1

Iv- (Q ) 1shy t

lt~ ~gt ~r- ~

-T (=7 T 1- ~gtl

Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd

(vI() p- f j~Pi

- Jli- (f) L= J-L

__i

l~ If~) ~ T

23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT

bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j

(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

rgt 1 bull (f~ ) ~() V (A I =_- ---

(p) 1shy

reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J

(1~ c no GCJ A PAaljrt tA~A 1 flczv A~

r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T

~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~

Jv C F) v Ir-( F( ~) ~ T

~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P

(lIJ tIt- (f) l Jf(fJ

lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~

t lID gt6 n-II~

X PtU () - I

( 1 t x B

- b( 1i f(i Imiddot l n i

r 1Y x (pYG) t C~ () c) I

it gt(~~ ~hC (t~ L )( C h n c

1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)

-iFt((~bC) (0dlCJ) b (~ nC)- --

PfC~ VJ tf1-) VlF0)

v r) ( [) ~ a r)_V --- I ok) ( P shyshy

1 plusmn T 1 T T ~

1- -j-T1shy I

IT 1 T T T T ~T) l 1-

T~I1 T T T L T T T)

1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy

-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l

- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-

L-JL-J --_---1

J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1

~ ) Cshy

_~ i1G f-CeVG ~c (A fJ)

J~ J~(- ~ ~

middotif ~ (J V f I

k

AQ~Jtt~ iA Jtf Je - i -

i

EE ihJ10~Q~-~X~ 1b~~~h~ ~~

ltJl

1~ b ~bU ( )) ~-=gt 1J ~ D 11

- ( fc (5 i

~ r

_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D

shy ~

fk

1 1

- L~-=-J-

L~0UC0 ~(~i

- - I

I) 1~1QJofL JA lt)

( Cv D) ~L

llt v ~ e fit ill

tr n

lJ

trU ~~) I

~~middotmiddotJ~~C6)- 1 bull

1~ A- J~)

t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)

A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj

JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A

t1 rf CF vl_ vr) (f J ~f) (

( AH0J)DtA L j j tk8HcrM AD HI

~ ft V f+l j V rt 11 I

blf J hUyjJ Pjf IJl L-1 1v CA)

-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~

lt2bJe ~ A-ltjTDJlOrlnj A

UVlU2ampO ft 15

M ~ t~JC~) bull p~~ cp (6)middot i i

~n(Orl~~ rsf~--Jb B~~ iI

0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j

I I i A~~rs r ~)~) iT~5~)~)

D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0

jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S

1 (Av rst~ liN ~~

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

-=It Fr ~ 1 r )

h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f

1 ~ rt-= 1+ ( I ~ t

-r~=

f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)

I I

i i i

l~l~~~~~ ~~ ~pMJI

I I I

(

-sJIt HlJ~

7 Iv- (PrJ) V Pn )

Fi L4-Cr) ~c r 7f 1(() - T

1 r ~ i Cf () ~Q

0K Hrp LA ~ n IIqtn r~ I hlf

v J

w ( ~ V jI

J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l

I -L i ti

l l-r T 1 l[ 1 ldJ 1 T [I

I

J r 1- T T j i- T i

I

I Tr I

I

T -- shy

J_ 1 11-I I

I I 1I

bull If V ~ (

Y1~ (f 0

~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)

~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)

~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )

-I -

TT -i 1 T

-I

r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

I _t _ shy

1 1 T T 1- 1shyT 1shyT iT T2- 1

i _I I

1 1 1 IJ- l- T

-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--

~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)

j (--1 f 1 ~l ~ l ()

reg

crJk)ttll tAUlll

i ~rl_

TVIHttmiddot~ H ~

~ TC~) ~)

X( G ~)J

~~ i

i16~i~(f)(L) ~

( tJ(~) ii

pF~~h) ~ F[PvfJI3) 1 (~) C~)

~o tiC f~(8) 11 rJ(p (1) J

h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

~ gtJ

6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ

~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl

I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z

i

=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 16: (JJ - alas.matf.bg.ac.rs

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8 ~-=-~~i

( nfl2bc[r6 ~1vl kC

t ~ ex (x~c) - -

-~ kJ)1~iKlftYKlA (~l(-J~_C~Jr~tgt~x lLJi fr(t ~i1cent 1)) e biyI--r) lt2

rshy1

shy

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lt)-

~(Almiddot Pc~

rJ- -~p~tA - - shy

I

shy (-j) -r---

I

r T I

1 ~_

0 1 1t b( 1 tlt E 1 ~E Z

K J ~ -- ~ ~

reg (jj P

r-~A~

( -oJ -J 11

D r )J ] ~~-~

(i) A Y =1-

+ (

~ J

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+1 -t ~ 7 )

I

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VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 17: (JJ - alas.matf.bg.ac.rs

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VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 18: (JJ - alas.matf.bg.ac.rs

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HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

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eN = 1

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RP(N) =~ (nonCKyn)

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= N x) eP(Ii) = 0

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b ~ ~ b b be c ebb ~

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X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

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X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 19: (JJ - alas.matf.bg.ac.rs

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eN = 1

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RP(N) =~ (nonCKyn)

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= N x) eP(Ii) = 0

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b ~ ~ b b be c ebb ~

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N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

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X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 20: (JJ - alas.matf.bg.ac.rs

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y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

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bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

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Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

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bull VxR(x x) V VxR(x x) v(lfFI I

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bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

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bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 21: (JJ - alas.matf.bg.ac.rs

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N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

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a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

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y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

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bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

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bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 22: (JJ - alas.matf.bg.ac.rs

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CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

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(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

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RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

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GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

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F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 23: (JJ - alas.matf.bg.ac.rs

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1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY

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r I)

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t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r

-rJ 1061 VlKA

(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA

r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c

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8~D=- 2513 +1CL

LS 2 = A62~ JO ~ t_ 50 l + ~2

o - 2- ~ 1 fJl (3pound5 I -==- ~8

n3~ -- 0

13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2

JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L

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CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J

bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

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c~ -~ rn lt~ -- t

)

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f1 I

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tt

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b X -= SA-=gt

X=7J~

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L~ )~ 1j ~ J

A- -~

reg ut(Vk-

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nOUlJV o -iVV I 0 ~ A

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l~c)J I

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I t A

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I

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A

M hA _ _

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I

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d J OJ

( r )

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v)J (~J J - (V U) ch

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100 - 2

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1 bull

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L X I - --

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I f

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fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

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dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

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reg L9A oj1 =-LO CA L C

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I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

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J J

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r)r

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r~ fh~

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(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

rgt 1 bull (f~ ) ~() V (A I =_- ---

(p) 1shy

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(1~ c no GCJ A PAaljrt tA~A 1 flczv A~

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t lID gt6 n-II~

X PtU () - I

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t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)

A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj

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( AH0J)DtA L j j tk8HcrM AD HI

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I I i A~~rs r ~)~) iT~5~)~)

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jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S

1 (Av rst~ liN ~~

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

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h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f

1 ~ rt-= 1+ ( I ~ t

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f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)

I I

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~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)

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TT -i 1 T

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r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

I _t _ shy

1 1 T T 1- 1shyT 1shyT iT T2- 1

i _I I

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j (--1 f 1 ~l ~ l ()

reg

crJk)ttll tAUlll

i ~rl_

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i16~i~(f)(L) ~

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pF~~h) ~ F[PvfJI3) 1 (~) C~)

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h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

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P-V(f1tieM j b~ orJ4 ()

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i

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1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

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2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

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L

eYOfy~Ptltj~JI f

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h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

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Page 24: (JJ - alas.matf.bg.ac.rs

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VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 25: (JJ - alas.matf.bg.ac.rs

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eN = 1

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= N x) eP(Ii) = 0

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N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

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a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

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X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 26: (JJ - alas.matf.bg.ac.rs

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N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

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a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

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y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

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bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

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- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

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bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 27: (JJ - alas.matf.bg.ac.rs

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1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY

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r I)

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t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r

-rJ 1061 VlKA

(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA

r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c

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8~D=- 2513 +1CL

LS 2 = A62~ JO ~ t_ 50 l + ~2

o - 2- ~ 1 fJl (3pound5 I -==- ~8

n3~ -- 0

13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2

JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L

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CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J

bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

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c~ -~ rn lt~ -- t

)

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f1 I

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tt

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b X -= SA-=gt

X=7J~

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L~ )~ 1j ~ J

A- -~

reg ut(Vk-

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nOUlJV o -iVV I 0 ~ A

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l~c)J I

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I t A

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I

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A

M hA _ _

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I

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d J OJ

( r )

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v)J (~J J - (V U) ch

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100 - 2

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1 bull

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L X I - --

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I f

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fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

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dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

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reg L9A oj1 =-LO CA L C

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I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

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J J

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r)r

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r~ fh~

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(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

rgt 1 bull (f~ ) ~() V (A I =_- ---

(p) 1shy

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(1~ c no GCJ A PAaljrt tA~A 1 flczv A~

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t lID gt6 n-II~

X PtU () - I

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t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)

A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj

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( AH0J)DtA L j j tk8HcrM AD HI

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I I i A~~rs r ~)~) iT~5~)~)

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jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S

1 (Av rst~ liN ~~

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

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h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f

1 ~ rt-= 1+ ( I ~ t

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f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)

I I

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~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)

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TT -i 1 T

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r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

I _t _ shy

1 1 T T 1- 1shyT 1shyT iT T2- 1

i _I I

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j (--1 f 1 ~l ~ l ()

reg

crJk)ttll tAUlll

i ~rl_

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i16~i~(f)(L) ~

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pF~~h) ~ F[PvfJI3) 1 (~) C~)

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h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

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P-V(f1tieM j b~ orJ4 ()

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i

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1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

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2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

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L

eYOfy~Ptltj~JI f

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h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

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bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

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- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

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jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

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bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 29: (JJ - alas.matf.bg.ac.rs

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= N x) eP(Ii) = 0

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N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

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3

bull S(G(e)))

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bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 30: (JJ - alas.matf.bg.ac.rs

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I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 31: (JJ - alas.matf.bg.ac.rs

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

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I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 32: (JJ - alas.matf.bg.ac.rs

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eN = 1

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RP(N) =~ (nonCKyn)

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= N x) eP(Ii) = 0

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2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

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X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

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X y ) ( a b

3

bull S(G(e)))

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bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 33: (JJ - alas.matf.bg.ac.rs

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dIV v d er d L tA d ~ - Q- L1

(l~ ~ d( -7 d)[ d (A

c)~~ r

v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_

~ rJ Ned ( t~

(~ - ir 1 ~ -tC~

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1 ~f1~ ()

(L r~ J -+ rt O Igt

cO

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r v---fI ~ ~ I

--

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J (T(0 TI~ J

r

tJ

bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ

8~D=- 2513 +1CL

LS 2 = A62~ JO ~ t_ 50 l + ~2

o - 2- ~ 1 fJl (3pound5 I -==- ~8

n3~ -- 0

13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2

JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L

~A

33) 3 1iY1 [5 v J1It~J A

r t I I reg 0 117t Vshy

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2

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p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)

~m I~j

l we~O

Q ~amp ~~~

u --~f 6 k()

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OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0

fA~ ~ Lj = ~ t 1- r-dj I X I J e i-

Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d

111-1

C -~d

S~ --+ ) 9A ~S--==0

CL = Me O-KZo M la-tr

CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J

bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

1= ~ 3 c

1~ --A~

reg 21=M

C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j

c~ -~ rn lt~ -- t

)

iv- ~

f1 I

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) J U-IQ

tt

J1Jh A r=A It k)

OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1

b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

nOUlJV o -iVV I 0 ~ A

~ 100 i11 1 1 0

~ i ~Iv - yYI

JA 2~b ~l=

l~c)J I

10 SAyoshy t~ b (0 ~i

J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )

-= - f5 - 2 )~~-

0 =tI f

~_O~L

m ~y-- (~l1J -J - ~ ~

(~3~A

) Y =c s h

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reg Gf~fr~ d~- J L1 (0 (1)

I t A

j )A (~)~ ~WC-~2~l)

I

1=M ~

b~-=~ U ~ ~ (A ~J I 1

1)(~

8f I) __

J ( lJ L(-I2 8 8raquo ~ 7

~I ~L

21 f t1shy

1 = c i

JI (Q~- 2_ lt-Gl VI v J

Q_ ~ -1 i) J 1 rebk hA i

JIJ ~ ) ~

CUC10 rP0e~-u---vj A

y - f l- L ~ =- rv b r3

J (111f)pound~)~ f1 I t1

)J =- ~l~ ~ VV _ L I

A

M hA _ _

IV_ tt

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olt0

I f- ~ c ~ ~ II

( 1-7 I

x =+ 1

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(NY

(25 j JshyM1 - ~ fAshy

~- G~

k ~--= (~ )~1 J = ~ 51 ~S-

j5K~ ~ ~ 8~ ~~ S - 3

I _

t

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10 ~ ~S S~ ~

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I

( - G(~ (~ vr c 111

~-J 0~C -~I

S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V

I f Ii c

y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J

I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~

Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull

( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij

d J OJ

( r )

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ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~

c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J

v)J (~J J - (V U) ch

j-A J ~)d l)cJJ ia d

1(t cZ I j

_ i I

I ~Jlt+~ L1JJrl-h~ Ii i

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)e GflJ~ ~~tt14 tt

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r ftX

k~

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J

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t r(M bull ~) ~ ( ~) j If (~)

~CC ~) ~ ~(L~r =~~~~~

1 i) ( ~-

(~ (X)) A

~ (~GO A

1(00 I

~ 2shy

100 - 2

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CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc

13~ L Co

~J ~~ -5 _j -==

AJlj 2- ~~_tL1f 312shy k ~N~~j -

v I1-

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t9~J -- 1shy

cf y ( ~ i-J ~~

~(1-) (-~-1 ) ~ - ~t

3~2 - Lmiddot (

1 bull

)

- ljx S

L X I - --

I - jtv ty- ~ rfl 2 a lr1 -iJ

~-v~ ---~ - l r A

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I f

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fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

d~c0

dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

-I 0

-t t) ) ~ 6--e~~~~ J~ oj

middot~middotLAi~V(

d

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l ( ()

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~ )

I 0

( ~ -1 ( )

reg L9A oj1 =-LO CA L C

u 1 ~ )

0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11

I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k

(JY61 i Jil~y 40

T -BQNlQ ~ 1J) ---J

ImiddotGS ~ 0

1 ~ --z11

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J J

j (J ~ky ~ -3 G

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JJrOl(ff-1 v A~ 1 ~f1

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W1 d

bltf L 1

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(1~lmiddot1l-t- 4 L - =

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- t

tmiddot

( I t

) J C ~

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11

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J

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I

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i V

f

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Y f 1 Z )l

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f ~ V

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et~ pound~O~Amiddot M rfkip1middot MA- Tf1

amp0 ~ AvA -II middot0

Y~7 ~(() Xl=X

~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~

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middotrv~(R) ~middot1

C c-C

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S~ p 2 I f i LK~- ~A CJ)064

lt VI 1 f

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1 (1-) fT I6 b f ~ e) A-t___ I I _

s

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~o r~ J11 flt

r)r

~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -

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lAY (( f ~) lw (A-) ~ j~lr C~)e

I tr ( tJ )) =IT (Ai V 111 (6)

r~ fh~

10u If) ~ T

1Ci lJ) ~ 1

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__i

l~ If~) ~ T

23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT

bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j

(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

rgt 1 bull (f~ ) ~() V (A I =_- ---

(p) 1shy

reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J

(1~ c no GCJ A PAaljrt tA~A 1 flczv A~

r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T

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Jv C F) v Ir-( F( ~) ~ T

~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P

(lIJ tIt- (f) l Jf(fJ

lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~

t lID gt6 n-II~

X PtU () - I

( 1 t x B

- b( 1i f(i Imiddot l n i

r 1Y x (pYG) t C~ () c) I

it gt(~~ ~hC (t~ L )( C h n c

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-iFt((~bC) (0dlCJ) b (~ nC)- --

PfC~ VJ tf1-) VlF0)

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1 plusmn T 1 T T ~

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IT 1 T T T T ~T) l 1-

T~I1 T T T L T T T)

1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy

-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l

- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-

L-JL-J --_---1

J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1

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middotif ~ (J V f I

k

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i

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shy ~

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tr n

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t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)

A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj

JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A

t1 rf CF vl_ vr) (f J ~f) (

( AH0J)DtA L j j tk8HcrM AD HI

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blf J hUyjJ Pjf IJl L-1 1v CA)

-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~

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~n(Orl~~ rsf~--Jb B~~ iI

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I I i A~~rs r ~)~) iT~5~)~)

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jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S

1 (Av rst~ liN ~~

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

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h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f

1 ~ rt-= 1+ ( I ~ t

-r~=

f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)

I I

i i i

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Fi L4-Cr) ~c r 7f 1(() - T

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v J

w ( ~ V jI

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l l-r T 1 l[ 1 ldJ 1 T [I

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J r 1- T T j i- T i

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J_ 1 11-I I

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Y1~ (f 0

~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)

~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)

~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )

-I -

TT -i 1 T

-I

r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

I _t _ shy

1 1 T T 1- 1shyT 1shyT iT T2- 1

i _I I

1 1 1 IJ- l- T

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j (--1 f 1 ~l ~ l ()

reg

crJk)ttll tAUlll

i ~rl_

TVIHttmiddot~ H ~

~ TC~) ~)

X( G ~)J

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i16~i~(f)(L) ~

( tJ(~) ii

pF~~h) ~ F[PvfJI3) 1 (~) C~)

~o tiC f~(8) 11 rJ(p (1) J

h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

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6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ

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I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z

i

=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

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2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

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L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 34: (JJ - alas.matf.bg.ac.rs

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VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 35: (JJ - alas.matf.bg.ac.rs

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jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 36: (JJ - alas.matf.bg.ac.rs

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bull I

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rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM

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fA= ~ ~L f1 no(1oj1 0ff ~ fA

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8~D=- 2513 +1CL

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I

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eN = 1

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= N x) eP(Ii) = 0

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2

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b ~ ~ b b be c ebb ~

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X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 37: (JJ - alas.matf.bg.ac.rs

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P-V(f1tieM j b~ orJ4 ()

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i

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1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

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L

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b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 38: (JJ - alas.matf.bg.ac.rs

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middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

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f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

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h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

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le - fr0JbCA f

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I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

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xC 5 i~)

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y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

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L

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h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 39: (JJ - alas.matf.bg.ac.rs

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 40: (JJ - alas.matf.bg.ac.rs

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1- 1

l f J -

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_ r1- - ~ I~ ~ J

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J ~~~ ~~--lt ~- --shy

~ I

1

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= -(n

J C-ZfJ l~ e --tk~Jmiddot gt (efco (70 v

r - r

L (~1 r(jI(~ 2 --

tV f- Il~e ~

-- --shyd (~) L - if I 11) 0

~tr

- I

--~-------r-~~--~~ middotmiddot~ -shy

I

i Vltj

1-J) V )30 JeLl l dCJ 1 i o

- - -j -~ I~jI v------( 9 7gt vv~o- VvltJSId u 1- - c)u Cmiddotvf h1 J~ ~~)-l ) U IJ CU

-~- yl- v - i - ) Jshy

[

t ~ ifshy _i 1~gtft- iJ 3(--1 le J

-11 LC() )i c ~-7 ~ rxiNjO Jo--Lfo-( - -ltJ J ~ i T J ~ - shy

~ ( V) ~ ~ i

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) I_ 0) Cj ~~7i7) V +-l) 9 ) l 10)

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j) -VI J53 Q(t~I ) I

~ Cl- Jc~ t -y 1+1 ) ~j-7l1lJ9 a ) L~ ~0al~d9 V v CiJ~ ~ oJu CV j r (-

( -I 0 ~ lt~ V-- J-- 11-

1 1 __ ~ bull ( I G[ i j --v 1- tjl C) ~d

Vi I l l

J -~ ---J ~ ) ~ J c)0)shy

c-middot I ______ J -lj_L-- - ~ J cmiddot ~ j C l) - I gt--I-()ryf IV--+ 4 ~v ~ J v

)- I- I c- l- shyc

I __ __ Jgt- ~--v~T(v-t~~- 2____ L

-rlcG-ltJo~~-_~li~Jr~~ bull~ 1v~) (i+ -o ~-lAI5 I _- shy

- j -- (-7 ) ( -i- _)~J - )_--- l~ - --- _L- ~ J ~

C1)_ lc ~_J -ZJrs-~i-i=- 0middot~ J~ ) ~~J ~gtJZr ~ I

C -Zshy I

shy1- -VI-J

L----v J 2- -T1-- FV shy

C -_ ))- L _( ~~ V_ l vshy

- ~ GvJ gtJ~_) _-- __ 1 v

-11 I

- -- - -) 1 _ __i +1 iV LmiddotLJG__-J IL ~_vy _~~J

~ -- -------- -- -- 1 - middotr _v_+~iT-u-- shy ~-~=-amp4

---- -(------~----- - - shy

---y

~ Vl 1-7 -- ___J_t_middotJmiddot~_1r --------- ~~0- ----Jl-(y-- ---- shy T (---~-l~ ----shy

-- ~ --V--i ---~-= J- 2- f -c=f~-~~_~-l1 -

1 ~ gtf J hj J itcmiddot -I~ ~ _gt l

tr-l t -~~~ J L

~

J I-j 0

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J J J r1~ 0- v ~ j -~-

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i y_l Ii ) T V V

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j J C r

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v V-rV I -

OIv 01h~L (vi) T (

r ~ l ~ 1 L o~_~-l ltoJ ~(1 v - C-~J -+ ~ l+ J- ~)-1

)

r vi d L J ~ i c L j U) v]~l - (

j ~J J U

J Ji f - L t I-~ ~- l J l_J

y-v-

v~~~O~ (0) I ~

W01 u I V -Zk- ~ ~v-3 - ~ tj -- ~3~ r -v L -~ i _ AJ

j + J - J ( IVG ~l18 i 1- t 1 lJ Ie)

c L t

I~~~ a deg1 H twog VI d)

~ shy

----~~--~-~------------ - ---~------ f~ ~ 0ffgt A~laquo~JV~~)I ~ v ~ 19 ) J - V ~ o~9 ~ v vraquo ~- I

Ot~o ~y~v~v~~ c I ~ degACJ ) -- j~ 0

v~ vv~ 3 - VI Q vj 1A C)- lo _ VD -- Vno )c

H- Ir~ V J

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1J h+ A

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Ii ~

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1r

20

J i I

i J

t 1

Jishy

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l-iA)

I CI -- V I

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2 ~-r

60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t

(Alt fl 00shyi) (xl ey - It

J 6 ~

et~ I

6) ~ (A or I - I

j

~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy

q= ej + ( q r C c v v I

r lt- fr

b(IJI ( M eshyI J

r~

-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~

H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J

(

crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(

(~Ie)

0- e62KA~hW9A-k)e S ( t1J i~ fl

(A V Ir o (0 ceCr _ _ t s

f-~~ ~ttVgVl

o~ Y ~ ~~ J~r~ ~ JO flr~TA

fPttl cp0 P0 A J~fJ

h i i

5tTh A~ LA_i

cg C(56f1~~

1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i

1rfl~c4gt lJ tlVTHh _I-Ai-Ayen

J(

o 1- t (l j- rt-toJ~e (1 ~_

1- f t ~ J

J n(~l

r nmiddot e-J--~ Of7 beibE ~~IA

f) -+1

np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16

1ltamp ~

flpQ~5r~)(

bull I

O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA

rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM

) v

fA= ~ ~L f1 no(1oj1 0ff ~ fA

Pc ICA

D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v

regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It

1gt vHA-- 1 (0 h1f1 1-10 tH-of 0

O~-i p~ j f- ~ ~ I

nI ~ ~ (G iA I~ lbt2~ 5J k

iF l-

I

~ l

( v 2 ~ = it il Ii

iyen rshy

-gt

ic

A p r Rin () iL ~ 1i

1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY

oJ1A ) J~D fA 0 [ JHA (It Gt +5

r I)

0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5

~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH

t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r

-rJ 1061 VlKA

(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA

r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c

1

t2L~~ (1 PI f m + 0

5

I

r~ amp 6 I ( je 1

I 1 I

Ie C jJ

poundPJlitshy

F~ ~ c

NidCtA~)

Q] o~ Q~~- C ~~~~e ~JC~ (~~~J ~~2-A (~Ir)

cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA

dIV v d er d L tA d ~ - Q- L1

(l~ ~ d( -7 d)[ d (A

c)~~ r

v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_

~ rJ Ned ( t~

(~ - ir 1 ~ -tC~

e~ ~1 I 1 rj if l lt2-

1 ~f1~ ()

(L r~ J -+ rt O Igt

cO

C-2 -- rl l -Ii r~ o

r v---fI ~ ~ I

--

IlVll elf~ ~(bIJ 611~ fhAl~ IA

J (T(0 TI~ J

r

tJ

bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ

8~D=- 2513 +1CL

LS 2 = A62~ JO ~ t_ 50 l + ~2

o - 2- ~ 1 fJl (3pound5 I -==- ~8

n3~ -- 0

13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2

JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L

~A

33) 3 1iY1 [5 v J1It~J A

r t I I reg 0 117t Vshy

I t

6 Aft

( 0

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lL0 shyJ

0 -

gt-n lt-~) J

h

2

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f

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p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)

~m I~j

l we~O

Q ~amp ~~~

u --~f 6 k()

rC~T AOkftN~o)

OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0

fA~ ~ Lj = ~ t 1- r-dj I X I J e i-

Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d

111-1

C -~d

S~ --+ ) 9A ~S--==0

CL = Me O-KZo M la-tr

CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J

bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

1= ~ 3 c

1~ --A~

reg 21=M

C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j

c~ -~ rn lt~ -- t

)

iv- ~

f1 I

~ Vvtz-t t G

) J U-IQ

tt

J1Jh A r=A It k)

OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1

b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

nOUlJV o -iVV I 0 ~ A

~ 100 i11 1 1 0

~ i ~Iv - yYI

JA 2~b ~l=

l~c)J I

10 SAyoshy t~ b (0 ~i

J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )

-= - f5 - 2 )~~-

0 =tI f

~_O~L

m ~y-- (~l1J -J - ~ ~

(~3~A

) Y =c s h

-I ) (~ ([~~

~J)en_pound nOJ ~jlle C J

reg Gf~fr~ d~- J L1 (0 (1)

I t A

j )A (~)~ ~WC-~2~l)

I

1=M ~

b~-=~ U ~ ~ (A ~J I 1

1)(~

8f I) __

J ( lJ L(-I2 8 8raquo ~ 7

~I ~L

21 f t1shy

1 = c i

JI (Q~- 2_ lt-Gl VI v J

Q_ ~ -1 i) J 1 rebk hA i

JIJ ~ ) ~

CUC10 rP0e~-u---vj A

y - f l- L ~ =- rv b r3

J (111f)pound~)~ f1 I t1

)J =- ~l~ ~ VV _ L I

A

M hA _ _

IV_ tt

~~ ~ A A 3~ LA -== II 5- -4 f

olt0

I f- ~ c ~ ~ II

( 1-7 I

x =+ 1

C-Oj ~ j~ ~ - ~S

(NY

(25 j JshyM1 - ~ fAshy

~- G~

k ~--= (~ )~1 J = ~ 51 ~S-

j5K~ ~ ~ 8~ ~~ S - 3

I _

t

bJ v -= _~ ( shyf 5 ~ A )3- l

10 ~ ~S S~ ~

~~k L S c

I

( - G(~ (~ vr c 111

~-J 0~C -~I

S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V

I f Ii c

y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J

I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~

Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull

( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij

d J OJ

( r )

( J I ~~ ~ 0

ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~

c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J

v)J (~J J - (V U) ch

j-A J ~)d l)cJJ ia d

1(t cZ I j

_ i I

I ~Jlt+~ L1JJrl-h~ Ii i

i

(IA) ~--~ ~ 53 VI

) -lQn~crto-

)e GflJ~ ~~tt14 tt

( ~l ~~l ~ L ~l~ 1

~

r ftX

k~

(lV1fD- G fOI D --I

J

2oo~

t r(M bull ~) ~ ( ~) j If (~)

~CC ~) ~ ~(L~r =~~~~~

1 i) ( ~-

(~ (X)) A

~ (~GO A

1(00 I

~ 2shy

100 - 2

~ (V) ) V) ( i ~ ~J

CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc

13~ L Co

~J ~~ -5 _j -==

AJlj 2- ~~_tL1f 312shy k ~N~~j -

v I1-

---shy1

t9~J -- 1shy

cf y ( ~ i-J ~~

~(1-) (-~-1 ) ~ - ~t

3~2 - Lmiddot (

1 bull

)

- ljx S

L X I - --

I - jtv ty- ~ rfl 2 a lr1 -iJ

~-v~ ---~ - l r A

- (Ml -shy-

I f

~ k -tampJ -= LA t CG t reg

fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

d~c0

dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

-I 0

-t t) ) ~ 6--e~~~~ J~ oj

middot~middotLAi~V(

d

~ t t2~~ l)

~ =0 -tL bull

c ~ )--ti

l ( ()

C0Q]) IAVI jEth f ~

2d (3 L I I-t S) - ~

~ )

I 0

( ~ -1 ( )

reg L9A oj1 =-LO CA L C

u 1 ~ )

0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11

I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k

(JY61 i Jil~y 40

T -BQNlQ ~ 1J) ---J

ImiddotGS ~ 0

1 ~ --z11

0 -

~ B ) ~~ ~ ~ ) I A (

J J

j (J ~ky ~ -3 G

0~ ~ G ~~~t

J -= - V Z-~~) - t ( tc-1)

JJrOl(ff-1 v A~ 1 ~f1

nbull bull -= tCshyv VI_

W1 d

bltf L 1

-=r

(1~lmiddot1l-t- 4 L - =

-

- t

tmiddot

( I t

) J C ~

-y ygt 1 f

) ~j v ~

1-- i

ff

11

N2-d( I

I)]

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(1 - It) middot -- 1~to

I X 10 cO xV A - i

Jlfr~~06V ~f-knA

(j f~) f- j J e

J

( Y j J I ~- X fltj

I

I~ l

i V

f

i j l f

Y f 1 Z )l

~ll+r Ul)4~~f)~4-~~QC_~[Atil11

f ~ V

] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_

-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA

et~ pound~O~Amiddot M rfkip1middot MA- Tf1

amp0 ~ AvA -II middot0

Y~7 ~(() Xl=X

~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~

- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -

Jz ~ - ~

CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J

11 ~~Lr)1 j~ = )lt K J

~0 )iV Y Kj) ~

-

middotrv~(R) ~middot1

C c-C

11 -no rV-tv~e -D he))N~re

S~ p 2 I f i LK~- ~A CJ)064

lt VI 1 f

~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~

~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~

1 (1-) fT I6 b f ~ e) A-t___ I I _

s

IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU

~o r~ J11 flt

r)r

~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -

UiJ)i = f

lAY (( f ~) lw (A-) ~ j~lr C~)e

I tr ( tJ )) =IT (Ai V 111 (6)

r~ fh~

10u If) ~ T

1Ci lJ) ~ 1

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1 (Av rst~ liN ~~

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( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

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f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

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h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

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le - fr0JbCA f

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xC 5 i~)

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y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

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L

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~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 41: (JJ - alas.matf.bg.ac.rs

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fA~ ~ Lj = ~ t 1- r-dj I X I J e i-

Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d

111-1

C -~d

S~ --+ ) 9A ~S--==0

CL = Me O-KZo M la-tr

CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J

bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

1= ~ 3 c

1~ --A~

reg 21=M

C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j

c~ -~ rn lt~ -- t

)

iv- ~

f1 I

~ Vvtz-t t G

) J U-IQ

tt

J1Jh A r=A It k)

OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1

b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

nOUlJV o -iVV I 0 ~ A

~ 100 i11 1 1 0

~ i ~Iv - yYI

JA 2~b ~l=

l~c)J I

10 SAyoshy t~ b (0 ~i

J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )

-= - f5 - 2 )~~-

0 =tI f

~_O~L

m ~y-- (~l1J -J - ~ ~

(~3~A

) Y =c s h

-I ) (~ ([~~

~J)en_pound nOJ ~jlle C J

reg Gf~fr~ d~- J L1 (0 (1)

I t A

j )A (~)~ ~WC-~2~l)

I

1=M ~

b~-=~ U ~ ~ (A ~J I 1

1)(~

8f I) __

J ( lJ L(-I2 8 8raquo ~ 7

~I ~L

21 f t1shy

1 = c i

JI (Q~- 2_ lt-Gl VI v J

Q_ ~ -1 i) J 1 rebk hA i

JIJ ~ ) ~

CUC10 rP0e~-u---vj A

y - f l- L ~ =- rv b r3

J (111f)pound~)~ f1 I t1

)J =- ~l~ ~ VV _ L I

A

M hA _ _

IV_ tt

~~ ~ A A 3~ LA -== II 5- -4 f

olt0

I f- ~ c ~ ~ II

( 1-7 I

x =+ 1

C-Oj ~ j~ ~ - ~S

(NY

(25 j JshyM1 - ~ fAshy

~- G~

k ~--= (~ )~1 J = ~ 51 ~S-

j5K~ ~ ~ 8~ ~~ S - 3

I _

t

bJ v -= _~ ( shyf 5 ~ A )3- l

10 ~ ~S S~ ~

~~k L S c

I

( - G(~ (~ vr c 111

~-J 0~C -~I

S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V

I f Ii c

y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J

I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~

Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull

( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij

d J OJ

( r )

( J I ~~ ~ 0

ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~

c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J

v)J (~J J - (V U) ch

j-A J ~)d l)cJJ ia d

1(t cZ I j

_ i I

I ~Jlt+~ L1JJrl-h~ Ii i

i

(IA) ~--~ ~ 53 VI

) -lQn~crto-

)e GflJ~ ~~tt14 tt

( ~l ~~l ~ L ~l~ 1

~

r ftX

k~

(lV1fD- G fOI D --I

J

2oo~

t r(M bull ~) ~ ( ~) j If (~)

~CC ~) ~ ~(L~r =~~~~~

1 i) ( ~-

(~ (X)) A

~ (~GO A

1(00 I

~ 2shy

100 - 2

~ (V) ) V) ( i ~ ~J

CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc

13~ L Co

~J ~~ -5 _j -==

AJlj 2- ~~_tL1f 312shy k ~N~~j -

v I1-

---shy1

t9~J -- 1shy

cf y ( ~ i-J ~~

~(1-) (-~-1 ) ~ - ~t

3~2 - Lmiddot (

1 bull

)

- ljx S

L X I - --

I - jtv ty- ~ rfl 2 a lr1 -iJ

~-v~ ---~ - l r A

- (Ml -shy-

I f

~ k -tampJ -= LA t CG t reg

fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

d~c0

dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

-I 0

-t t) ) ~ 6--e~~~~ J~ oj

middot~middotLAi~V(

d

~ t t2~~ l)

~ =0 -tL bull

c ~ )--ti

l ( ()

C0Q]) IAVI jEth f ~

2d (3 L I I-t S) - ~

~ )

I 0

( ~ -1 ( )

reg L9A oj1 =-LO CA L C

u 1 ~ )

0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11

I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k

(JY61 i Jil~y 40

T -BQNlQ ~ 1J) ---J

ImiddotGS ~ 0

1 ~ --z11

0 -

~ B ) ~~ ~ ~ ) I A (

J J

j (J ~ky ~ -3 G

0~ ~ G ~~~t

J -= - V Z-~~) - t ( tc-1)

JJrOl(ff-1 v A~ 1 ~f1

nbull bull -= tCshyv VI_

W1 d

bltf L 1

-=r

(1~lmiddot1l-t- 4 L - =

-

- t

tmiddot

( I t

) J C ~

-y ygt 1 f

) ~j v ~

1-- i

ff

11

N2-d( I

I)]

~ ( 1

(1 - It) middot -- 1~to

I X 10 cO xV A - i

Jlfr~~06V ~f-knA

(j f~) f- j J e

J

( Y j J I ~- X fltj

I

I~ l

i V

f

i j l f

Y f 1 Z )l

~ll+r Ul)4~~f)~4-~~QC_~[Atil11

f ~ V

] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_

-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA

et~ pound~O~Amiddot M rfkip1middot MA- Tf1

amp0 ~ AvA -II middot0

Y~7 ~(() Xl=X

~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~

- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -

Jz ~ - ~

CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J

11 ~~Lr)1 j~ = )lt K J

~0 )iV Y Kj) ~

-

middotrv~(R) ~middot1

C c-C

11 -no rV-tv~e -D he))N~re

S~ p 2 I f i LK~- ~A CJ)064

lt VI 1 f

~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~

~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~

1 (1-) fT I6 b f ~ e) A-t___ I I _

s

IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU

~o r~ J11 flt

r)r

~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -

UiJ)i = f

lAY (( f ~) lw (A-) ~ j~lr C~)e

I tr ( tJ )) =IT (Ai V 111 (6)

r~ fh~

10u If) ~ T

1Ci lJ) ~ 1

Iv- (Q ) 1shy t

lt~ ~gt ~r- ~

-T (=7 T 1- ~gtl

Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd

(vI() p- f j~Pi

- Jli- (f) L= J-L

__i

l~ If~) ~ T

23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT

bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j

(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

rgt 1 bull (f~ ) ~() V (A I =_- ---

(p) 1shy

reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J

(1~ c no GCJ A PAaljrt tA~A 1 flczv A~

r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T

~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~

Jv C F) v Ir-( F( ~) ~ T

~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P

(lIJ tIt- (f) l Jf(fJ

lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~

t lID gt6 n-II~

X PtU () - I

( 1 t x B

- b( 1i f(i Imiddot l n i

r 1Y x (pYG) t C~ () c) I

it gt(~~ ~hC (t~ L )( C h n c

1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)

-iFt((~bC) (0dlCJ) b (~ nC)- --

PfC~ VJ tf1-) VlF0)

v r) ( [) ~ a r)_V --- I ok) ( P shyshy

1 plusmn T 1 T T ~

1- -j-T1shy I

IT 1 T T T T ~T) l 1-

T~I1 T T T L T T T)

1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy

-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l

- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-

L-JL-J --_---1

J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1

~ ) Cshy

_~ i1G f-CeVG ~c (A fJ)

J~ J~(- ~ ~

middotif ~ (J V f I

k

AQ~Jtt~ iA Jtf Je - i -

i

EE ihJ10~Q~-~X~ 1b~~~h~ ~~

ltJl

1~ b ~bU ( )) ~-=gt 1J ~ D 11

- ( fc (5 i

~ r

_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D

shy ~

fk

1 1

- L~-=-J-

L~0UC0 ~(~i

- - I

I) 1~1QJofL JA lt)

( Cv D) ~L

llt v ~ e fit ill

tr n

lJ

trU ~~) I

~~middotmiddotJ~~C6)- 1 bull

1~ A- J~)

t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)

A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj

JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A

t1 rf CF vl_ vr) (f J ~f) (

( AH0J)DtA L j j tk8HcrM AD HI

~ ft V f+l j V rt 11 I

blf J hUyjJ Pjf IJl L-1 1v CA)

-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~

lt2bJe ~ A-ltjTDJlOrlnj A

UVlU2ampO ft 15

M ~ t~JC~) bull p~~ cp (6)middot i i

~n(Orl~~ rsf~--Jb B~~ iI

0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j

I I i A~~rs r ~)~) iT~5~)~)

D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0

jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S

1 (Av rst~ liN ~~

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

-=It Fr ~ 1 r )

h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f

1 ~ rt-= 1+ ( I ~ t

-r~=

f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)

I I

i i i

l~l~~~~~ ~~ ~pMJI

I I I

(

-sJIt HlJ~

7 Iv- (PrJ) V Pn )

Fi L4-Cr) ~c r 7f 1(() - T

1 r ~ i Cf () ~Q

0K Hrp LA ~ n IIqtn r~ I hlf

v J

w ( ~ V jI

J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l

I -L i ti

l l-r T 1 l[ 1 ldJ 1 T [I

I

J r 1- T T j i- T i

I

I Tr I

I

T -- shy

J_ 1 11-I I

I I 1I

bull If V ~ (

Y1~ (f 0

~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)

~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)

~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )

-I -

TT -i 1 T

-I

r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

I _t _ shy

1 1 T T 1- 1shyT 1shyT iT T2- 1

i _I I

1 1 1 IJ- l- T

-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--

~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)

j (--1 f 1 ~l ~ l ()

reg

crJk)ttll tAUlll

i ~rl_

TVIHttmiddot~ H ~

~ TC~) ~)

X( G ~)J

~~ i

i16~i~(f)(L) ~

( tJ(~) ii

pF~~h) ~ F[PvfJI3) 1 (~) C~)

~o tiC f~(8) 11 rJ(p (1) J

h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

~ gtJ

6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ

~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl

I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z

i

=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 42: (JJ - alas.matf.bg.ac.rs

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middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 43: (JJ - alas.matf.bg.ac.rs

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60tpJ tr 6M~ AtdJ ~JL E- C Kth eumiddotJrA cA Ar eFtV t

(Alt fl 00shyi) (xl ey - It

J 6 ~

et~ I

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j

~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy

q= ej + ( q r C c v v I

r lt- fr

b(IJI ( M eshyI J

r~

-A- eJ)lJ jfr12 6pJl(fIlieJto f J d ~ ~ d~

H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J

(

crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(

(~Ie)

0- e62KA~hW9A-k)e S ( t1J i~ fl

(A V Ir o (0 ceCr _ _ t s

f-~~ ~ttVgVl

o~ Y ~ ~~ J~r~ ~ JO flr~TA

fPttl cp0 P0 A J~fJ

h i i

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cg C(56f1~~

1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i

1rfl~c4gt lJ tlVTHh _I-Ai-Ayen

J(

o 1- t (l j- rt-toJ~e (1 ~_

1- f t ~ J

J n(~l

r nmiddot e-J--~ Of7 beibE ~~IA

f) -+1

np-eltflo efTAi llVI lLA j (lrv0 V )11 n fa VI 3 16

1ltamp ~

flpQ~5r~)(

bull I

O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA

rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM

) v

fA= ~ ~L f1 no(1oj1 0ff ~ fA

Pc ICA

D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v

regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It

1gt vHA-- 1 (0 h1f1 1-10 tH-of 0

O~-i p~ j f- ~ ~ I

nI ~ ~ (G iA I~ lbt2~ 5J k

iF l-

I

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iyen rshy

-gt

ic

A p r Rin () iL ~ 1i

1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY

oJ1A ) J~D fA 0 [ JHA (It Gt +5

r I)

0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5

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t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r

-rJ 1061 VlKA

(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA

r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c

1

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5

I

r~ amp 6 I ( je 1

I 1 I

Ie C jJ

poundPJlitshy

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cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA

dIV v d er d L tA d ~ - Q- L1

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J (T(0 TI~ J

r

tJ

bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ

8~D=- 2513 +1CL

LS 2 = A62~ JO ~ t_ 50 l + ~2

o - 2- ~ 1 fJl (3pound5 I -==- ~8

n3~ -- 0

13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2

JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L

~A

33) 3 1iY1 [5 v J1It~J A

r t I I reg 0 117t Vshy

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2

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p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)

~m I~j

l we~O

Q ~amp ~~~

u --~f 6 k()

rC~T AOkftN~o)

OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0

fA~ ~ Lj = ~ t 1- r-dj I X I J e i-

Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d

111-1

C -~d

S~ --+ ) 9A ~S--==0

CL = Me O-KZo M la-tr

CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J

bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

1= ~ 3 c

1~ --A~

reg 21=M

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c~ -~ rn lt~ -- t

)

iv- ~

f1 I

~ Vvtz-t t G

) J U-IQ

tt

J1Jh A r=A It k)

OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1

b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

nOUlJV o -iVV I 0 ~ A

~ 100 i11 1 1 0

~ i ~Iv - yYI

JA 2~b ~l=

l~c)J I

10 SAyoshy t~ b (0 ~i

J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )

-= - f5 - 2 )~~-

0 =tI f

~_O~L

m ~y-- (~l1J -J - ~ ~

(~3~A

) Y =c s h

-I ) (~ ([~~

~J)en_pound nOJ ~jlle C J

reg Gf~fr~ d~- J L1 (0 (1)

I t A

j )A (~)~ ~WC-~2~l)

I

1=M ~

b~-=~ U ~ ~ (A ~J I 1

1)(~

8f I) __

J ( lJ L(-I2 8 8raquo ~ 7

~I ~L

21 f t1shy

1 = c i

JI (Q~- 2_ lt-Gl VI v J

Q_ ~ -1 i) J 1 rebk hA i

JIJ ~ ) ~

CUC10 rP0e~-u---vj A

y - f l- L ~ =- rv b r3

J (111f)pound~)~ f1 I t1

)J =- ~l~ ~ VV _ L I

A

M hA _ _

IV_ tt

~~ ~ A A 3~ LA -== II 5- -4 f

olt0

I f- ~ c ~ ~ II

( 1-7 I

x =+ 1

C-Oj ~ j~ ~ - ~S

(NY

(25 j JshyM1 - ~ fAshy

~- G~

k ~--= (~ )~1 J = ~ 51 ~S-

j5K~ ~ ~ 8~ ~~ S - 3

I _

t

bJ v -= _~ ( shyf 5 ~ A )3- l

10 ~ ~S S~ ~

~~k L S c

I

( - G(~ (~ vr c 111

~-J 0~C -~I

S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V

I f Ii c

y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J

I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~

Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull

( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij

d J OJ

( r )

( J I ~~ ~ 0

ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~

c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J

v)J (~J J - (V U) ch

j-A J ~)d l)cJJ ia d

1(t cZ I j

_ i I

I ~Jlt+~ L1JJrl-h~ Ii i

i

(IA) ~--~ ~ 53 VI

) -lQn~crto-

)e GflJ~ ~~tt14 tt

( ~l ~~l ~ L ~l~ 1

~

r ftX

k~

(lV1fD- G fOI D --I

J

2oo~

t r(M bull ~) ~ ( ~) j If (~)

~CC ~) ~ ~(L~r =~~~~~

1 i) ( ~-

(~ (X)) A

~ (~GO A

1(00 I

~ 2shy

100 - 2

~ (V) ) V) ( i ~ ~J

CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc

13~ L Co

~J ~~ -5 _j -==

AJlj 2- ~~_tL1f 312shy k ~N~~j -

v I1-

---shy1

t9~J -- 1shy

cf y ( ~ i-J ~~

~(1-) (-~-1 ) ~ - ~t

3~2 - Lmiddot (

1 bull

)

- ljx S

L X I - --

I - jtv ty- ~ rfl 2 a lr1 -iJ

~-v~ ---~ - l r A

- (Ml -shy-

I f

~ k -tampJ -= LA t CG t reg

fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

d~c0

dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

-I 0

-t t) ) ~ 6--e~~~~ J~ oj

middot~middotLAi~V(

d

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~ =0 -tL bull

c ~ )--ti

l ( ()

C0Q]) IAVI jEth f ~

2d (3 L I I-t S) - ~

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I 0

( ~ -1 ( )

reg L9A oj1 =-LO CA L C

u 1 ~ )

0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11

I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k

(JY61 i Jil~y 40

T -BQNlQ ~ 1J) ---J

ImiddotGS ~ 0

1 ~ --z11

0 -

~ B ) ~~ ~ ~ ) I A (

J J

j (J ~ky ~ -3 G

0~ ~ G ~~~t

J -= - V Z-~~) - t ( tc-1)

JJrOl(ff-1 v A~ 1 ~f1

nbull bull -= tCshyv VI_

W1 d

bltf L 1

-=r

(1~lmiddot1l-t- 4 L - =

-

- t

tmiddot

( I t

) J C ~

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11

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I X 10 cO xV A - i

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I

I~ l

i V

f

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Y f 1 Z )l

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f ~ V

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et~ pound~O~Amiddot M rfkip1middot MA- Tf1

amp0 ~ AvA -II middot0

Y~7 ~(() Xl=X

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middotrv~(R) ~middot1

C c-C

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S~ p 2 I f i LK~- ~A CJ)064

lt VI 1 f

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1 (1-) fT I6 b f ~ e) A-t___ I I _

s

IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU

~o r~ J11 flt

r)r

~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -

UiJ)i = f

lAY (( f ~) lw (A-) ~ j~lr C~)e

I tr ( tJ )) =IT (Ai V 111 (6)

r~ fh~

10u If) ~ T

1Ci lJ) ~ 1

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(vI() p- f j~Pi

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l~ If~) ~ T

23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT

bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j

(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

rgt 1 bull (f~ ) ~() V (A I =_- ---

(p) 1shy

reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J

(1~ c no GCJ A PAaljrt tA~A 1 flczv A~

r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T

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Jv C F) v Ir-( F( ~) ~ T

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(lIJ tIt- (f) l Jf(fJ

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t lID gt6 n-II~

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it gt(~~ ~hC (t~ L )( C h n c

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t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)

A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj

JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A

t1 rf CF vl_ vr) (f J ~f) (

( AH0J)DtA L j j tk8HcrM AD HI

~ ft V f+l j V rt 11 I

blf J hUyjJ Pjf IJl L-1 1v CA)

-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~

lt2bJe ~ A-ltjTDJlOrlnj A

UVlU2ampO ft 15

M ~ t~JC~) bull p~~ cp (6)middot i i

~n(Orl~~ rsf~--Jb B~~ iI

0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j

I I i A~~rs r ~)~) iT~5~)~)

D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0

jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S

1 (Av rst~ liN ~~

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

-=It Fr ~ 1 r )

h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f

1 ~ rt-= 1+ ( I ~ t

-r~=

f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)

I I

i i i

l~l~~~~~ ~~ ~pMJI

I I I

(

-sJIt HlJ~

7 Iv- (PrJ) V Pn )

Fi L4-Cr) ~c r 7f 1(() - T

1 r ~ i Cf () ~Q

0K Hrp LA ~ n IIqtn r~ I hlf

v J

w ( ~ V jI

J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l

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l l-r T 1 l[ 1 ldJ 1 T [I

I

J r 1- T T j i- T i

I

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I

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J_ 1 11-I I

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bull If V ~ (

Y1~ (f 0

~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)

~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)

~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )

-I -

TT -i 1 T

-I

r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

I _t _ shy

1 1 T T 1- 1shyT 1shyT iT T2- 1

i _I I

1 1 1 IJ- l- T

-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--

~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)

j (--1 f 1 ~l ~ l ()

reg

crJk)ttll tAUlll

i ~rl_

TVIHttmiddot~ H ~

~ TC~) ~)

X( G ~)J

~~ i

i16~i~(f)(L) ~

( tJ(~) ii

pF~~h) ~ F[PvfJI3) 1 (~) C~)

~o tiC f~(8) 11 rJ(p (1) J

h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

~ gtJ

6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ

~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl

I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z

i

=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 44: (JJ - alas.matf.bg.ac.rs

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(Alt fl 00shyi) (xl ey - It

J 6 ~

et~ I

6) ~ (A or I - I

j

~ () -IIlIfJ I(Ql6Vdl)1)1 ff 6PJ (V1shy

q= ej + ( q r C c v v I

r lt- fr

b(IJI ( M eshyI J

r~

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H~ bet~ ~~~1411ltJ Ilt 0t~NtJ middot6hlf~t cZ t )e J

(

crJIJmiddot 3~)~A HIi 11ltUl AeJ)UQ(AUHA brl-jeOA- d A Gmiddot NLct(

(~Ie)

0- e62KA~hW9A-k)e S ( t1J i~ fl

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f-~~ ~ttVgVl

o~ Y ~ ~~ J~r~ ~ JO flr~TA

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h i i

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1 ())VILAXshy_ - ~_ bull~ ~ bull_ __ __ ~~_i

1rfl~c4gt lJ tlVTHh _I-Ai-Ayen

J(

o 1- t (l j- rt-toJ~e (1 ~_

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1ltamp ~

flpQ~5r~)(

bull I

O(J-~ ~~~f PrfvCM~LA~~ GoJIG f ~ illfON bfj N-0110-0 Jeft ffOI 1((lt Hb (A M fAO() euroA) AA

rlfE-pound- c AQ VIviD Iflb lf8 Vl~amp A DP cr LA f Gf~ eM

) v

fA= ~ ~L f1 no(1oj1 0ff ~ fA

Pc ICA

D~ 6v J ( kl v fA 0A 6f0JC t3A r1- -(Jy Je Ii v

regoctO)ioECL wpn1lt0 1-hOr u ry-ocV gtlt to ~sl It

1gt vHA-- 1 (0 h1f1 1-10 tH-of 0

O~-i p~ j f- ~ ~ I

nI ~ ~ (G iA I~ lbt2~ 5J k

iF l-

I

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iyen rshy

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ic

A p r Rin () iL ~ 1i

1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY

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r I)

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t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r

-rJ 1061 VlKA

(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA

r~(b VI)Oll n 6 P~jcflt CoiLT A JC I5f~ u c

1

t2L~~ (1 PI f m + 0

5

I

r~ amp 6 I ( je 1

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Ie C jJ

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cAlC ~1 ( VM~J J~~ 6M ~gj~JVu~iA

dIV v d er d L tA d ~ - Q- L1

(l~ ~ d( -7 d)[ d (A

c)~~ r

v ~~Pj ~~h~ 11_ ~i ~e_~ 0 r-~ Eh ~ ) ~J hefI ANAil_

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J (T(0 TI~ J

r

tJ

bf)f V~ ~f- HfSi~Vrj 0 IiVI0 ko IJ 61IJ Avl K it oJ

8~D=- 2513 +1CL

LS 2 = A62~ JO ~ t_ 50 l + ~2

o - 2- ~ 1 fJl (3pound5 I -==- ~8

n3~ -- 0

13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2

JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L

~A

33) 3 1iY1 [5 v J1It~J A

r t I I reg 0 117t Vshy

I t

6 Aft

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lL0 shyJ

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p-~ O_~- 6- t V1rl1eJ-O AA-~ Q ~ iblfjiIgt1 (0 ~94jf)l1 vn(n1A)

~m I~j

l we~O

Q ~amp ~~~

u --~f 6 k()

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OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0

fA~ ~ Lj = ~ t 1- r-dj I X I J e i-

Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d

111-1

C -~d

S~ --+ ) 9A ~S--==0

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CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J

bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

1= ~ 3 c

1~ --A~

reg 21=M

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c~ -~ rn lt~ -- t

)

iv- ~

f1 I

~ Vvtz-t t G

) J U-IQ

tt

J1Jh A r=A It k)

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b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

nOUlJV o -iVV I 0 ~ A

~ 100 i11 1 1 0

~ i ~Iv - yYI

JA 2~b ~l=

l~c)J I

10 SAyoshy t~ b (0 ~i

J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )

-= - f5 - 2 )~~-

0 =tI f

~_O~L

m ~y-- (~l1J -J - ~ ~

(~3~A

) Y =c s h

-I ) (~ ([~~

~J)en_pound nOJ ~jlle C J

reg Gf~fr~ d~- J L1 (0 (1)

I t A

j )A (~)~ ~WC-~2~l)

I

1=M ~

b~-=~ U ~ ~ (A ~J I 1

1)(~

8f I) __

J ( lJ L(-I2 8 8raquo ~ 7

~I ~L

21 f t1shy

1 = c i

JI (Q~- 2_ lt-Gl VI v J

Q_ ~ -1 i) J 1 rebk hA i

JIJ ~ ) ~

CUC10 rP0e~-u---vj A

y - f l- L ~ =- rv b r3

J (111f)pound~)~ f1 I t1

)J =- ~l~ ~ VV _ L I

A

M hA _ _

IV_ tt

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olt0

I f- ~ c ~ ~ II

( 1-7 I

x =+ 1

C-Oj ~ j~ ~ - ~S

(NY

(25 j JshyM1 - ~ fAshy

~- G~

k ~--= (~ )~1 J = ~ 51 ~S-

j5K~ ~ ~ 8~ ~~ S - 3

I _

t

bJ v -= _~ ( shyf 5 ~ A )3- l

10 ~ ~S S~ ~

~~k L S c

I

( - G(~ (~ vr c 111

~-J 0~C -~I

S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V

I f Ii c

y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J

I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~

Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull

( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij

d J OJ

( r )

( J I ~~ ~ 0

ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~

c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J

v)J (~J J - (V U) ch

j-A J ~)d l)cJJ ia d

1(t cZ I j

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I ~Jlt+~ L1JJrl-h~ Ii i

i

(IA) ~--~ ~ 53 VI

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)e GflJ~ ~~tt14 tt

( ~l ~~l ~ L ~l~ 1

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r ftX

k~

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2oo~

t r(M bull ~) ~ ( ~) j If (~)

~CC ~) ~ ~(L~r =~~~~~

1 i) ( ~-

(~ (X)) A

~ (~GO A

1(00 I

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100 - 2

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CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc

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AJlj 2- ~~_tL1f 312shy k ~N~~j -

v I1-

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cf y ( ~ i-J ~~

~(1-) (-~-1 ) ~ - ~t

3~2 - Lmiddot (

1 bull

)

- ljx S

L X I - --

I - jtv ty- ~ rfl 2 a lr1 -iJ

~-v~ ---~ - l r A

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I f

~ k -tampJ -= LA t CG t reg

fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

d~c0

dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

-I 0

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middot~middotLAi~V(

d

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c ~ )--ti

l ( ()

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reg L9A oj1 =-LO CA L C

u 1 ~ )

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I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

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(JY61 i Jil~y 40

T -BQNlQ ~ 1J) ---J

ImiddotGS ~ 0

1 ~ --z11

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J J

j (J ~ky ~ -3 G

0~ ~ G ~~~t

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JJrOl(ff-1 v A~ 1 ~f1

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W1 d

bltf L 1

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(1~lmiddot1l-t- 4 L - =

-

- t

tmiddot

( I t

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 45: (JJ - alas.matf.bg.ac.rs

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 46: (JJ - alas.matf.bg.ac.rs

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OC06lf~e 1) (~- t V C ~ d 0 ~ro- J0

fA~ ~ Lj = ~ t 1- r-dj I X I J e i-

Gf ~=)I~ fLS lA (J-~ ~ ~~ - X c j c- ~ ~ - (=- e- -t d

111-1

C -~d

S~ --+ ) 9A ~S--==0

CL = Me O-KZo M la-tr

CD OAf-d8-t [)~TVt x-r Artv n fLA A e h e f~J

bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

1= ~ 3 c

1~ --A~

reg 21=M

C)lt = ~c4 gts~1 r ~ t [I ~V Olf ~ [L ~y K )~E tIJ lJ L ~ ~ t j

c~ -~ rn lt~ -- t

)

iv- ~

f1 I

~ Vvtz-t t G

) J U-IQ

tt

J1Jh A r=A It k)

OgtPrA JeA pN11A~1~ ti eJ-lI A reltJJe It 1

b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

nOUlJV o -iVV I 0 ~ A

~ 100 i11 1 1 0

~ i ~Iv - yYI

JA 2~b ~l=

l~c)J I

10 SAyoshy t~ b (0 ~i

J(O ( BAIL bG) ~ f 6 5 (- 1-9) 1-1 S-b ~ 2 )

-= - f5 - 2 )~~-

0 =tI f

~_O~L

m ~y-- (~l1J -J - ~ ~

(~3~A

) Y =c s h

-I ) (~ ([~~

~J)en_pound nOJ ~jlle C J

reg Gf~fr~ d~- J L1 (0 (1)

I t A

j )A (~)~ ~WC-~2~l)

I

1=M ~

b~-=~ U ~ ~ (A ~J I 1

1)(~

8f I) __

J ( lJ L(-I2 8 8raquo ~ 7

~I ~L

21 f t1shy

1 = c i

JI (Q~- 2_ lt-Gl VI v J

Q_ ~ -1 i) J 1 rebk hA i

JIJ ~ ) ~

CUC10 rP0e~-u---vj A

y - f l- L ~ =- rv b r3

J (111f)pound~)~ f1 I t1

)J =- ~l~ ~ VV _ L I

A

M hA _ _

IV_ tt

~~ ~ A A 3~ LA -== II 5- -4 f

olt0

I f- ~ c ~ ~ II

( 1-7 I

x =+ 1

C-Oj ~ j~ ~ - ~S

(NY

(25 j JshyM1 - ~ fAshy

~- G~

k ~--= (~ )~1 J = ~ 51 ~S-

j5K~ ~ ~ 8~ ~~ S - 3

I _

t

bJ v -= _~ ( shyf 5 ~ A )3- l

10 ~ ~S S~ ~

~~k L S c

I

( - G(~ (~ vr c 111

~-J 0~C -~I

S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V

I f Ii c

y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J

I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~

Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull

( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij

d J OJ

( r )

( J I ~~ ~ 0

ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~

c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J

v)J (~J J - (V U) ch

j-A J ~)d l)cJJ ia d

1(t cZ I j

_ i I

I ~Jlt+~ L1JJrl-h~ Ii i

i

(IA) ~--~ ~ 53 VI

) -lQn~crto-

)e GflJ~ ~~tt14 tt

( ~l ~~l ~ L ~l~ 1

~

r ftX

k~

(lV1fD- G fOI D --I

J

2oo~

t r(M bull ~) ~ ( ~) j If (~)

~CC ~) ~ ~(L~r =~~~~~

1 i) ( ~-

(~ (X)) A

~ (~GO A

1(00 I

~ 2shy

100 - 2

~ (V) ) V) ( i ~ ~J

CDUAPeo lA CGTfiIU I1flA P ellotlh) l1fJ Pc

13~ L Co

~J ~~ -5 _j -==

AJlj 2- ~~_tL1f 312shy k ~N~~j -

v I1-

---shy1

t9~J -- 1shy

cf y ( ~ i-J ~~

~(1-) (-~-1 ) ~ - ~t

3~2 - Lmiddot (

1 bull

)

- ljx S

L X I - --

I - jtv ty- ~ rfl 2 a lr1 -iJ

~-v~ ---~ - l r A

- (Ml -shy-

I f

~ k -tampJ -= LA t CG t reg

fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

d~c0

dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

-I 0

-t t) ) ~ 6--e~~~~ J~ oj

middot~middotLAi~V(

d

~ t t2~~ l)

~ =0 -tL bull

c ~ )--ti

l ( ()

C0Q]) IAVI jEth f ~

2d (3 L I I-t S) - ~

~ )

I 0

( ~ -1 ( )

reg L9A oj1 =-LO CA L C

u 1 ~ )

0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11

I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

-1r~--( ~ +b (1-)- L~t~+21-(t-~) ==~ t+ k

(JY61 i Jil~y 40

T -BQNlQ ~ 1J) ---J

ImiddotGS ~ 0

1 ~ --z11

0 -

~ B ) ~~ ~ ~ ) I A (

J J

j (J ~ky ~ -3 G

0~ ~ G ~~~t

J -= - V Z-~~) - t ( tc-1)

JJrOl(ff-1 v A~ 1 ~f1

nbull bull -= tCshyv VI_

W1 d

bltf L 1

-=r

(1~lmiddot1l-t- 4 L - =

-

- t

tmiddot

( I t

) J C ~

-y ygt 1 f

) ~j v ~

1-- i

ff

11

N2-d( I

I)]

~ ( 1

(1 - It) middot -- 1~to

I X 10 cO xV A - i

Jlfr~~06V ~f-knA

(j f~) f- j J e

J

( Y j J I ~- X fltj

I

I~ l

i V

f

i j l f

Y f 1 Z )l

~ll+r Ul)4~~f)~4-~~QC_~[Atil11

f ~ V

] )lOV-UOA-lA ~A-J~ ~ ~ eV-I61t fJJ tgtJA iO -1 A beAmiddot A V V f~ 60 J o~_

-fr ~P ft- ~f1tlr~JlJ qo fA toC 01 0- CC t~ A o 0 ~E- fT b Ill IfV- f- f6i~e Qil ~ R~ -10 ( iJ1 ~euA

et~ pound~O~Amiddot M rfkip1middot MA- Tf1

amp0 ~ AvA -II middot0

Y~7 ~(() Xl=X

~1 O-Ztlt) v ~ ~y 0- IZK D ~ j ~ ~

- 0 J Xv ~ ~ A 1 ~ Y I ( ~ I 1) - 1 1 ~ -

Jz ~ - ~

CKi ) f 1 ~ ~ tJ) [c lA )j) - (X ~ yJ v J ~ 0 vJ = J

11 ~~Lr)1 j~ = )lt K J

~0 )iV Y Kj) ~

-

middotrv~(R) ~middot1

C c-C

11 -no rV-tv~e -D he))N~re

S~ p 2 I f i LK~- ~A CJ)064

lt VI 1 f

~g~~ Cl(ffike bull ~oF~J)e A eJ 0JV~ 1 )Lj f f- C S IA lK ro~ eV ~offvlJ~

~~ ~roJ ft bullfj fI(j((~1-e copf00J e ~ f-- Lj 1 - M At f 6 4c v ~

1 (1-) fT I6 b f ~ e) A-t___ I I _

s

IfCK(gtj~e ~OfM)Je (~10(j P0t) cA C fNlgtU

~o r~ J11 flt

r)r

~e-8 5~j ~uVl~ i- Ie ~Jvlt-u VmiddotSgt C -

UiJ)i = f

lAY (( f ~) lw (A-) ~ j~lr C~)e

I tr ( tJ )) =IT (Ai V 111 (6)

r~ fh~

10u If) ~ T

1Ci lJ) ~ 1

Iv- (Q ) 1shy t

lt~ ~gt ~r- ~

-T (=7 T 1- ~gtl

Poaf VI IIpnre)l i~ l tvjO~ j e 4gtoP~) )fd

(vI() p- f j~Pi

- Jli- (f) L= J-L

__i

l~ If~) ~ T

23 b~ f I Jr J h K M~O A lt+ Jlt ~ 00 a rJ JV I0 fi cry (bII~J ~V Ay-j ~0(1 (t1 V rttr (I~ cT

bull~~ j f~r J j f LfI1IeJO 1- ~ ~ 0III( A VI (yj JC~ OJ Ir Cc i j

(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

rgt 1 bull (f~ ) ~() V (A I =_- ---

(p) 1shy

reg~uKPrgtA~ lA ~ - jQ lr v (f t l) Y- f (0 klf A~ V ~U LJ r h -J

(1~ c no GCJ A PAaljrt tA~A 1 flczv A~

r~ ( f (f ( ~)~ F~) ~ t l-u ( f v (f -J-)) LmiddotIIT It ) ~ T

~~ Jru- (~ V If ~)) ~ 1 J1 (~ )= ~

Jv C F) v Ir-( F( ~) ~ T

~ S or (f) -- ~ 1 ( f ~ ) ~J- ~ II IJ_~) ~ J P

(lIJ tIt- (f) l Jf(fJ

lY~ f V l f f d-)) =L 1gt (f~ ~ r Cf) J V (f C~) =1 IA h te J~

t lID gt6 n-II~

X PtU () - I

( 1 t x B

- b( 1i f(i Imiddot l n i

r 1Y x (pYG) t C~ () c) I

it gt(~~ ~hC (t~ L )( C h n c

1lt (~_~~ y~~- L~gt (Xf Pr J X tCS) Ji (K f f Yc-C)

-iFt((~bC) (0dlCJ) b (~ nC)- --

PfC~ VJ tf1-) VlF0)

v r) ( [) ~ a r)_V --- I ok) ( P shyshy

1 plusmn T 1 T T ~

1- -j-T1shy I

IT 1 T T T T ~T) l 1-

T~I1 T T T L T T T)

1- l J I T -L 1 l T 1 - I- TT 1- T 1 1 T 1shy 1shy

-r IT 1- T 1 1- TI -I shy 1 1 JshyI - l

- l T 1 J- ~I 1- 1 1shy1- i- 1 1- 1- 1shy 1 1- 1 ll-

L-JL-J --_---1

J 1Qo(jfc fr ~~ ~~ld t1 eGA bMJ rr1J)~Jl1

~ ) Cshy

_~ i1G f-CeVG ~c (A fJ)

J~ J~(- ~ ~

middotif ~ (J V f I

k

AQ~Jtt~ iA Jtf Je - i -

i

EE ihJ10~Q~-~X~ 1b~~~h~ ~~

ltJl

1~ b ~bU ( )) ~-=gt 1J ~ D 11

- ( fc (5 i

~ r

_-~~~~ (A(~t[-Aie4ofHtlM~1 -O~ hVb Pt=7C[ Ib D

shy ~

fk

1 1

- L~-=-J-

L~0UC0 ~(~i

- - I

I) 1~1QJofL JA lt)

( Cv D) ~L

llt v ~ e fit ill

tr n

lJ

trU ~~) I

~~middotmiddotJ~~C6)- 1 bull

1~ A- J~)

t Cpoundgtr) I J(e) It~) vJ~Q)~ L v J 1 f c~ r~ ko ~J 1cV t5-ltf 1rcO f M AJ iAk ~igt0ft~ f- (Kif cP~)

A 1 AI- f f~ f 1 A~ (A Ac +I cJj f fL fj

JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A

t1 rf CF vl_ vr) (f J ~f) (

( AH0J)DtA L j j tk8HcrM AD HI

~ ft V f+l j V rt 11 I

blf J hUyjJ Pjf IJl L-1 1v CA)

-- rhO PAl I 1 e Al AI-r ~ 1[ j j ~

lt2bJe ~ A-ltjTDJlOrlnj A

UVlU2ampO ft 15

M ~ t~JC~) bull p~~ cp (6)middot i i

~n(Orl~~ rsf~--Jb B~~ iI

0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j

I I i A~~rs r ~)~) iT~5~)~)

D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0

jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S

1 (Av rst~ liN ~~

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

-=It Fr ~ 1 r )

h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f

1 ~ rt-= 1+ ( I ~ t

-r~=

f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

ll ~c ~ H (1 -IF 1 1)1 (1- ~ 1 (~)

I I

i i i

l~l~~~~~ ~~ ~pMJI

I I I

(

-sJIt HlJ~

7 Iv- (PrJ) V Pn )

Fi L4-Cr) ~c r 7f 1(() - T

1 r ~ i Cf () ~Q

0K Hrp LA ~ n IIqtn r~ I hlf

v J

w ( ~ V jI

J~JI l ~ r_l-P~~) ( _~ r) TT[T- ~ I I - i I I I I l

I -L i ti

l l-r T 1 l[ 1 ldJ 1 T [I

I

J r 1- T T j i- T i

I

I Tr I

I

T -- shy

J_ 1 11-I I

I I 1I

bull If V ~ (

Y1~ (f 0

~_ t) l ( Pf- ~~ r~ 1) V Cf l ~ f () V (l f ( ~_ f r)

~ ~ i 1 () V ( l r l~ t ) Y (1 PA lt ~l r)

~)middot85 (r cy (e ~) ~ Cr (r -~7 ~) )

-I -

TT -i 1 T

-I

r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

I _t _ shy

1 1 T T 1- 1shyT 1shyT iT T2- 1

i _I I

1 1 1 IJ- l- T

-r- l 1 T(J) 1 T 1 1 T~L -r 1 T t L---J 6 1 LJL--

~J (f f r--() 1 lf~ i -l d j ( f -l~ t---l ) v (l plJ~ ~ l r) I (1 pr l~ f r)

j (--1 f 1 ~l ~ l ()

reg

crJk)ttll tAUlll

i ~rl_

TVIHttmiddot~ H ~

~ TC~) ~)

X( G ~)J

~~ i

i16~i~(f)(L) ~

( tJ(~) ii

pF~~h) ~ F[PvfJI3) 1 (~) C~)

~o tiC f~(8) 11 rJ(p (1) J

h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

~ gtJ

6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ

~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl

I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z

i

=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 47: (JJ - alas.matf.bg.ac.rs

1fCoJi fVl IIkf ~ 1 6rj 0 MtJ J cA 0 rJi I(A 6 i IH I f il j Iiegtlr 111iY

oJ1A ) J~D fA 0 [ JHA (It Gt +5

r I)

0))C ()i~r)Aflt11 0Q (Jilt Tf AM a tr-= OlL G1-+ 5

~ Glk+~) r5 =shyf Pr~0JC Ih 1-1 ent-+fplH

t ~1lt~ (jA(~ ilioC bQgt1 VbJi lj V~A- G Ie T 5 lAM n- nr0ci A -JlIA Ji AU Llt 0Ta r

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(iV) 6 if c~A eJA~ LA nO[lrt3iO r bPilt- 61)-1 vO~ 110 Ao I-r A (5Jrl c r 06Jj II KA

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o - 2- ~ 1 fJl (3pound5 I -==- ~8

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)

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X=7J~

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L~ )~ 1j ~ J

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I t A

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I

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d J OJ

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1 bull

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I f

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j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

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I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

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rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

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(p) 1shy

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t lID gt6 n-II~

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1 (Av rst~ liN ~~

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( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

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l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

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f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

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II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

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r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

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j (--1 f 1 ~l ~ l ()

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)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

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P-V(f1tieM j b~ orJ4 ()

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middotlaquo(~1 e) V1 R(Y-I e)

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eYOfy~Ptltj~JI f

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h~PJfeuro1)~1~~ 1

Ii i ii J

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b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 48: (JJ - alas.matf.bg.ac.rs

NidCtA~)

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8~D=- 2513 +1CL

LS 2 = A62~ JO ~ t_ 50 l + ~2

o - 2- ~ 1 fJl (3pound5 I -==- ~8

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13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2

JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L

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bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

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)

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tt

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L~ )~ 1j ~ J

A- -~

reg ut(Vk-

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1 bull

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I f

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j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

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I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 49: (JJ - alas.matf.bg.ac.rs

--

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J (T(0 TI~ J

r

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8~D=- 2513 +1CL

LS 2 = A62~ JO ~ t_ 50 l + ~2

o - 2- ~ 1 fJl (3pound5 I -==- ~8

n3~ -- 0

13 jo ~r2- -= 30 - (~ 102 - gO) shy 2-middotz 51y I 61 c Lmiddot 2 52 - 2

JlC4fl1A- t ~ L S 2 - - JA f3 -+ ~ ) L

~A

33) 3 1iY1 [5 v J1It~J A

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111-1

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bull 30 I2 -~3

() - 2L -~~

rf 2 _ ~ ~1~ 112

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)

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tt

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b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

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~ 100 i11 1 1 0

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JA 2~b ~l=

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10 SAyoshy t~ b (0 ~i

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I t A

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A

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1 bull

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L X I - --

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I f

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j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

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l ( ()

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reg L9A oj1 =-LO CA L C

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I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

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(JY61 i Jil~y 40

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ImiddotGS ~ 0

1 ~ --z11

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J J

j (J ~ky ~ -3 G

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JJrOl(ff-1 v A~ 1 ~f1

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W1 d

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tmiddot

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r~ fh~

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VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 50: (JJ - alas.matf.bg.ac.rs

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 51: (JJ - alas.matf.bg.ac.rs

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bull 30 I2 -~3

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VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 52: (JJ - alas.matf.bg.ac.rs

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rf 2 _ ~ ~1~ 112

16 ~L -- ( - 0 2amp - n AL t) b _~ L 11~

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1~ --A~

reg 21=M

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c~ -~ rn lt~ -- t

)

iv- ~

f1 I

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) J U-IQ

tt

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b X -= SA-=gt

X=7J~

(h J) ~ A r~---~---(

L~ )~ 1j ~ J

A- -~

reg ut(Vk-

(A I rli )= 1

nOUlJV o -iVV I 0 ~ A

~ 100 i11 1 1 0

~ i ~Iv - yYI

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10 SAyoshy t~ b (0 ~i

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I t A

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Q_ ~ -1 i) J 1 rebk hA i

JIJ ~ ) ~

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y - f l- L ~ =- rv b r3

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1 bull

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I f

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j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

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I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

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r)r

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r~ fh~

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rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

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(p) 1shy

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t lID gt6 n-II~

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VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 53: (JJ - alas.matf.bg.ac.rs

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L~ )~ 1j ~ J

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reg ut(Vk-

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10 SAyoshy t~ b (0 ~i

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1 bull

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L X I - --

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j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

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I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

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r)r

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(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

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t lID gt6 n-II~

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( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

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rt f ~ K hf v h H~

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middotlaquo(~1 e) V1 R(Y-I e)

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VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 54: (JJ - alas.matf.bg.ac.rs

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VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 55: (JJ - alas.matf.bg.ac.rs

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( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

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f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

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r T T T I -I- 1 1 D T(lJ 1shy~ T 1 1 1

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j (--1 f 1 ~l ~ l ()

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i ~rl_

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pF~~h) ~ F[PvfJI3) 1 (~) C~)

~o tiC f~(8) 11 rJ(p (1) J

h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

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le - fr0JbCA f

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P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

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i

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1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

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y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

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L

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h~PJfeuro1)~1~~ 1

Ii i ii J

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b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 56: (JJ - alas.matf.bg.ac.rs

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j5K~ ~ ~ 8~ ~~ S - 3

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t lID gt6 n-II~

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middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

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f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

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i _I I

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j (--1 f 1 ~l ~ l ()

reg

crJk)ttll tAUlll

i ~rl_

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( tJ(~) ii

pF~~h) ~ F[PvfJI3) 1 (~) C~)

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h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

~ gtJ

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~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl

I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

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i

=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

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L

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h~PJfeuro1)~1~~ 1

Ii i ii J

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b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 57: (JJ - alas.matf.bg.ac.rs

( - G(~ (~ vr c 111

~-J 0~C -~I

S I ( F Z -- 1- I( I J v 08 V ~- (CJ~ V) J187 v ~V

I f Ii c

y v) r~ -vi V1 ~ G - lI - ~(~f -v) ~r ~J

I gt1 --y t~ ~- V) vr~ ~ - ( ~d~ -~d) I v(~ Yd) =~

Y - ~ )0 I 71gt ~ - ~i4 ~ 11 bull

( ~J) (~lJ) J r ~(~ v) 1 ~ 0 gtA - Ij

d J OJ

( r )

( J I ~~ ~ 0

ilJ)od u ~d ~J ~ 7J ~d VIlf ~Ir v~

c~ d) d _~-)OJJ ~I dv-) - ~d y= (u W ) 0~ V J

v)J (~J J - (V U) ch

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1(00 I

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v I1-

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t9~J -- 1shy

cf y ( ~ i-J ~~

~(1-) (-~-1 ) ~ - ~t

3~2 - Lmiddot (

1 bull

)

- ljx S

L X I - --

I - jtv ty- ~ rfl 2 a lr1 -iJ

~-v~ ---~ - l r A

- (Ml -shy-

I f

~ k -tampJ -= LA t CG t reg

fI-~K0 ~JJR)blgt- l-Jl I ~~ IAM- -j GKj 0j 1

_~~ol(tlt) = d 10 d==-c (J-~-tei=dJ J

d~c0

dl) d(

j e6 If ~ P-t 0 ao rft~rop ATamp A HI

d

-I 0

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middot~middotLAi~V(

d

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c ~ )--ti

l ( ()

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2d (3 L I I-t S) - ~

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reg L9A oj1 =-LO CA L C

u 1 ~ )

0 ~i~ LA ~ 20middot (-0~) -f 5~i - ~ So + 50 t~ io~11

I u lO ~ 1 ~ 2f L 2-20 - Lr-ishy

l ~ (it 1 2 r- 0) ~ 5 ltJ -t (~ S -r 8 )-1- jJ

+- lt fV-II f-shy -

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(JY61 i Jil~y 40

T -BQNlQ ~ 1J) ---J

ImiddotGS ~ 0

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j (J ~ky ~ -3 G

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JJrOl(ff-1 v A~ 1 ~f1

nbull bull -= tCshyv VI_

W1 d

bltf L 1

-=r

(1~lmiddot1l-t- 4 L - =

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 58: (JJ - alas.matf.bg.ac.rs

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 59: (JJ - alas.matf.bg.ac.rs

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 60: (JJ - alas.matf.bg.ac.rs

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

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I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

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GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

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GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 61: (JJ - alas.matf.bg.ac.rs

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)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

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~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 62: (JJ - alas.matf.bg.ac.rs

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+- lt fV-II f-shy -

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 63: (JJ - alas.matf.bg.ac.rs

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rt f ~ K hf v h H~

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VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 64: (JJ - alas.matf.bg.ac.rs

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 65: (JJ - alas.matf.bg.ac.rs

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VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 66: (JJ - alas.matf.bg.ac.rs

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CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

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GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

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F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 67: (JJ - alas.matf.bg.ac.rs

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)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

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xC 5 i~)

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~ (fl)A b) x CA~lAltO)

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y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

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X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

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L

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h~PJfeuro1)~1~~ 1

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b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 68: (JJ - alas.matf.bg.ac.rs

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rt f ~ K hf v h H~

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crJk)ttll tAUlll

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~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 69: (JJ - alas.matf.bg.ac.rs

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 70: (JJ - alas.matf.bg.ac.rs

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(lj0s )nu) Ylfrl~ V ttr(F) =1 ~ O~ cf0pru1JJ +1bull bull J J

rb~SJ p()j~ ~n- ~0j (~~1 Hill

I I

rgt 1 bull (f~ ) ~() V (A I =_- ---

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t lID gt6 n-II~

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I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

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=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

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xC 5 i~)

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i

middotlaquo(~1 e) V1 R(Y-I e)

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L

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b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 71: (JJ - alas.matf.bg.ac.rs

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)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

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i

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1~ F1b) 1~ T( ~J b)

xC 5 i~)

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~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 72: (JJ - alas.matf.bg.ac.rs

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=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

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xC 5 i~)

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middotlaquo(~1 e) V1 R(Y-I e)

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b _~ 1tf c Ci pj C1(11J ~ shy

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VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 73: (JJ - alas.matf.bg.ac.rs

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JJI9A- je tACtCfDl10 GfJOfO u)1A 1fI o6A

t1 rf CF vl_ vr) (f J ~f) (

( AH0J)DtA L j j tk8HcrM AD HI

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blf J hUyjJ Pjf IJl L-1 1v CA)

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UVlU2ampO ft 15

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~n(Orl~~ rsf~--Jb B~~ iI

0811 ~-ltAlgtlAcfhl I tAeuro eJaG0fhAeI1L24j

I I i A~~rs r ~)~) iT~5~)~)

D fL ~ 1 e1Wq ~ k (ItT~ (l vJ4 el-tJfrA r 0

jj ttQK OAr IJQr~e nfW~lti~0ek1lA ((AK~) bullllj-l[S

1 (Av rst~ liN ~~

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

-=It Fr ~ 1 r )

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( l F ) l gtbullbull1 f) r ( l (~ r) J f) 2

II ~ v l t ~I f) ~ (IIt ~ f ~ v r ~ (l f 1 ( l (~) ~ 1~ f p)

k~ ~ f ~ (1 f f t 1~ (l-gt J Ie) ~ (It f f) = (7p 7) f lr (T~i Vr ~~~f~Qf~ 1 jf))jl(1--~ r~ (l~J f~j 1) fi llf J0 v (~ I -) l~) v ( l~ 1r ) f j

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1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

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y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

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L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 74: (JJ - alas.matf.bg.ac.rs

middot 5) ~ JAcent f ~ l (lJ[ c) ~ (A- 1 ) V ( II - c)

( ~ y L) 1 A- = ( s~ ~-) v (( 1 A-)

~(~~ k V (b r c) =-~ vE) ( (F+ If c)

l2J c)v ~ (0( rt) ~ (Cr Aj

rt f ~ K hf v h H~

lp=- ~J v (II f ) (l f ~ ~) v lt l PI li f 1

-( I -7 pVJ ( prf) f f -1 ~~

-=It Fr ~ 1 r )

h ( r ( ~ ~ -- (If v~t) ( Iflt VC) - f

1 ~ rt-= 1+ ( I ~ t

-r~=

f lr (ct -lp~) ~ ( ~ ~l)~) f) ~

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 75: (JJ - alas.matf.bg.ac.rs

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3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 76: (JJ - alas.matf.bg.ac.rs

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xC 5 i~)

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i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

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eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

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b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 77: (JJ - alas.matf.bg.ac.rs

~ TC~) ~)

X( G ~)J

~~ i

i16~i~(f)(L) ~

( tJ(~) ii

pF~~h) ~ F[PvfJI3) 1 (~) C~)

~o tiC f~(8) 11 rJ(p (1) J

h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

~ gtJ

6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ

~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl

I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z

i

=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 78: (JJ - alas.matf.bg.ac.rs

~~ i

i16~i~(f)(L) ~

( tJ(~) ii

pF~~h) ~ F[PvfJI3) 1 (~) C~)

~o tiC f~(8) 11 rJ(p (1) J

h~middot F(t)(~) I~ r (t)(g) 1~F(pv~) (~) ~4 (fIf~) (~)

)( (~( ~o) y (vtAl) ~b Flr) t~4) A8 FCp)( tis)

1+r-LJJ eft ~) 11 IFl vr) ell )

X(r~+) x ( f-1d j]

le - fr0JbCA f

~ gtJ

6olkon AJlV 1 foJpAllfte F+OOA~J~vO()GJ~~cCP~~1~iJ

~fl(rA l ~f OH2Jv ~J VJ~ofV1e JkAp4ftJ (12 4 CflTI P~ ce )ltApbll-Ifl

I CAA C)~lp ~IetLTt-k AA ijfA~0Iv ~tJmiddotlAAA f A p rltY) 1 Pft-4 ~~o ~ i p jv M~pAfv ~~~ J GVQt1(6 Oi I

P-V(f1tieM j b~ orJ4 ()

iJjampt~J f~ ~Or L1 Ute

3~p~~-hj~~-~4plli4b ~ jJfl~ I1c ~J rl0 ~f) ~ (~~rJA(Z

i

=[ ~0 f J ~ ) (f7rld t~S bull Ul-tJT (-gt7 PJ 1 T ( (~fJ pound9 (j -~ rj ~ ( 9 ~)iS)~ (~ (A)

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 79: (JJ - alas.matf.bg.ac.rs

1~ F1b) 1~ T( ~J b)

xC 5 i~)

(hP(~)( B) 1 TUJ (0)

~ (fl)A b) x CA~lAltO)

2AtItJ 3 l~ TCs)(J) 2l1 Tht)(

y (A 111 0 ) 2 CYCi ~)XAJIL3) 2-~_FLt(2 X Cl1L2)

i

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 80: (JJ - alas.matf.bg.ac.rs

middotlaquo(~1 e) V1 R(Y-I e)

VXj~J tltl Kj) -- ~fMl~J A

X CR t(ltL~ltj1J ~( ~)) ~-~ ~ ~

-i~0pMPlr-r-ePk

L

eYOfy~Ptltj~JI f

i(fL It~)I bull

h~PJfeuro1)~1~~ 1

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 81: (JJ - alas.matf.bg.ac.rs

Ii i ii J

[

b _~ 1tf c Ci pj C1(11J ~ shy

~yS J- middotmiddotv 1

VI

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 82: (JJ - alas.matf.bg.ac.rs

3aAaT~U HCJlOrl1iKH fJcO je3I1Ka nelJI1KaTCKOr patIYHa npBOr pena 4HHe

CrrelJehH cI1M6mUf Re1c = R S Funpound = P G Canstpound= e rrpI1 qeMY

jear(R)=ar(F) 2ar(S)=ar(G) 1 (i) KojJI je on crre)Jenlfx Hlf30Ba ClfM60na TepM KOjlf cpopMyna a KOjI1

HR je)JJw HM JPYro F(G(x) G(y)) S(F(x G(e)) R(x S(x)) R(e e) VyR(x e) Vx3yR(x y) Vx(R(x G(y)) = P(x v))

(ii) 3a CBaKO nojaBJhl1Balhe npOMeHiblfBe Y cpopMynH o[(penHTI1 [(a nll je

OHO Cn060lJHO HnI1 Be3aHO

V(R(x y) 1 3y(R(T y) = S(x)) ix(R(x u) 1 =JuR(z v)) V R(x v)

(iii) J(aTlf je3HK je lfHTepnpeTlfpaH Ha cKynOBI1Ma Z N peN) M X X=ab)c

I1HTeprrpeTalmja Ha Z

RZ =~ (ypeljeIbe ueJIHX 6pojeBa)

SZ _ nufilll il01WllWWH = 1 2 3 4 pz + (ca6I1palhe uenllx 6pojeBa)

GZ = g npI1 qeMY je 9 7l -+ Z H g(x) = ~x x E Z Z e = O

I1HTepnpeTaUHja Ha N

RN I (lJeibHBOCT npI1pOlJHI1X 6pojelm)

SN 6ufiiu flpocUl = 2 3 5 711 pN = (MHO)Kelhe nplfpOAHHX 6pojeBa)

GN = h npH qeMY je h N ---t N 11 h(x) 2x + 1 x E N

eN = 1

I1l-nepnpeTaQHja Ha peN)

RP(N) =~ (nonCKyn)

SP(N) = 6uUlu KOHQ4arl- pP(N) n (npeceK cKynoBa)

GP(N) C lKOMnneMeHT cKyna y OlJHOCY Ha N C peN) ---t P(N) Ii

= N x) eP(Ii) = 0

I1HTepnpeTaQHja Ha X

RX = (a c) (bc)(cc)(ab) SX acl~

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 83: (JJ - alas.matf.bg.ac.rs

2

= npH qeMY je 6HHapHa OnepaUHja J]CcentHHMCaHa Ta6rrHUOM

b ~ ~ b b be c ebb ~

GX = e npH qeMY je eX -+ X J]aTO ca

a be) e ( a a a

(a) OrrpellJUM BpellHOCTH TepMa

F(F(x e) G(y)) G(F(x x)) F(G(x) G(x)) y

X y )- Z rrpH BarryaUHjH npOMeHJbHBHX fL = -2 1 (

N npH BarryaUHjH npOMeHJbHBHX fL (~i ) )

- P(N) npH BanyaUHjH npOMeHJbHBHX fL = ( 1~2 2~3

a )X npH BarryaUHjH npOMeHJbHBHX fL X yb (

(6) HcnHTaTH TaIHOCnpopMyrra R( F(x e) G(y)) H S(F(x x ))=R( G(x) G(y))

y (x y ) - Z rrpH BarryaIlHjH npOMeHJbHBHX fL = -2 1

X Y )N npH BarryaUHjH npOMeHJbHBHX fL ( 2 1

) - P(N) npH BaJIyaIlHjH npOMeHJbHBHX fL = ( 1~2 2~3

X y ) ( a b

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe

Page 84: (JJ - alas.matf.bg.ac.rs

3

bull S(G(e)))

bull VxVV(S(x) 1 S(y) = S(F(x y))) bull VxVy(R(x y) = R(G(y) G(x))) Vx(S(x) 3yR(xF(xy)))

bull VxVy(R(x y) v R(y x)) penOM Y MoneJIHMa Z N peN) X (r) PeqeHHItar-m gaTOr je3HKa H3pa3HTH crreLlena cBojCTBa CTpYKType N

- flpOU360q q6a upocflla 6poja liuje ilpocUi 6poj

- CBaKU upocia 6poj 6ehu oq 2je HeilapaH

Cn) PeqeHHuaMa )laTor je3HKa H3pa3HTH CJIeLlena cBojCTBa CTpyKType

P(N) - KOMillleMeuUi KOIW4H02 cKyila liuje KOIta4aH cKyil

- llpeceK q6a KOfla1f1a cKyuaje KOHa4a1t CKyU

- fiocf]Joju cKyii f(oju JJuje KOHa4QIl U LUjU KOMilneMeliiil Huje f(OHQ-lQH

(I)) 3a CBaKY OJ( HapeJJHHX peqem1ua JJeqJHHHCaTil (aKO je TO Moryoe) 6ap

jeJ1JIY ilHTeprrperaUHjy je3HKa rrpH KOjOj je Ta pe1JeHHHa TaqHa H 6ap jellHY

HHTeprrpeTaUIJY IIpH ROJOJ peqeHHua HHJe TaqHa

bull Vx8(x) A VxR(x x) = Vx(8(x) A R(x c 1lt Jli tof r IFJlt r hi ILJ~(i

bull VxR(x x) V VxR(x x) v(lfFI I

I) 3xS(x) V 3xR(x x) = 3(8(x) V R(x x))

bull Vx(R(xx) V R(xx)) (e) Koje cy on CJIeneOHX peqeHHua naTor je3HKa BaJhaHe

bull VxB(x) 1 VxR(x x) = Vx(8(x) 1 R(x x))

bull 3x(R(x x) = S(x)) bull Vx--R(x x) bull 3x8(x) V 3xR(x x) 3x(8(x) V R(x x)) bull Vx(R(x x) V R(x x)) bull Vx3y(S(x) V 8(y)) cent VxVy( -gtBe