M1401 เซต2014

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. 02 9962692 1

1. ก 2

2. ก ∈∈∈∈ 53. ก! "

#.

!ก$%&%'()*+ 115. ,)&&%()*+

5.1 - 13

5.2 ก'*ก!+ 1

5.3 ก'-'*ก!+ 1"

/. 0$%) !!! 2

. กก''+

.1

4 22

.2 !!,6 25

.3 0*+,!&%& 32

. &-' 7,% 7&& 55

". ก-8&6ก9:960$%) !!! /1

1. %)! /5

11.

ก)&6ก!+11.1 0$%) !!! 5

11.2 4 #

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1. ก

!"#!$ %&' () *!+%, ('!"#!$ %-*! '%"/-*' (- (' !$ % *!+ (-/%' !$ %

&'3# (34- %"# !$ %&'353 3'3 3$7 383- 3$ 3*!+3'

( (' ก

&% /- 2 *

1. ก--ก+&6ก

%3'33%: ;< =< > 4E&'5?% (' 10 -33 F > G

% (F 3 5+&3 F-3 F

H 4E&'!&-- (' 5 I2I -33 F H G

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2. ก---!ก+; 7!

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. 02 9962692 M

2 5&'/4 F*', ('/&&'%

1. {2< −N}

2. {1< I< N< O

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2. ก ∈∈∈∈

!"# ' (3% (' D 4E%&' ,' ' &*-3:!3 ∈

" N 4E%&' ; ,' ' ; &*- N∈ ;" S /%4E%&' ; ,' /%' ; &*- S∉ ;

; G {2< I< {2}< {1< 2}< N}

5+ 2∈ ; I∈ ;{2} ∈ ; {1< 2} ∈ ;N∈ ; 6∉ ;O∉ ; {I} ∉ ;

; 4E (%% N 3 &*- TU;V G N

" ; G {M< N< 6< O} 5+/- TU;V G

" = G {1< {I}} 5+/- TU=V G

" > G { } 5+/- TU>V G

" H G {{2< I< M}} 5+/- TUHV G

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3 5&*-4E%&' (- '%3 F'5%

1. ; G {1< 2< I} 2. = G {2< I< M}

I. > G {1< {2}< I< M} M. H G {1< {1}< {1< 2}< I}

N. J G {1< {1< 2}< {1}< {2}< I< M} 6. L G {I< M< {2< {I}}< 6< S}

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O. P G {2IM} S. W G {X∈ YX 4E5 (' I}

9. Z G {QQ 4E5?% (' + 11 *!+ 1N}

'!-,)&9 = +;!ก,!-' 7>4ก!+' 78

1. - ; G {0< 1< {0< 1}} &'-"'. {0} ∈ ;

&. {0< 1} ∈ ;

. {{0< 1}} ∈ ;

. {0< {1}} ∈ ;

2. ; G {Q2Q G X< X∈ +Z } &**5*5%/--3&'-. {2< M< 6< S

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I. &'-"'

. {QQ∈ +Z *!+ 1Q2 − G 0} &**5*5%/-4E {1< −1}

&. {2< M< 6< S} &*', ('/&/-4E {QQ 4E5 (' 10} . ; G {−2} & ; *', ('/&/-4E {QQ∈Z ('-!'3% 2QIQ2 2 −+ G 0}

. {1< 2< I< M

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3. ก!

(%"'/-*'%5%- 53- ('5% (*'/%/- '3

; G {@< [< \< ]< ^} 4E %5%

= G {1< 2< I< M G {QQ 4E5?% (%%−I *' M}

G 4E %5%

H G {QQ 4E55 *!+ 1

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'!-,)&9 = +;!ก,!-' 7>4ก!+' 78

1. &'-4E53-

. {QQ 4E5$- 1 F}

&. {QQ∈Z *!+ 2Q G 2}

. {Q−1 ≤ Q ≤ 0}

. {QQ G IT *!+ 1 ≤ T ≤ N}

2. &'-/%4E'3

. {QQ∈` a 2Q G 2T< T∈ +Z }

&. {Q 1Q2 + G 0a Q∈` }

. {Q 1Q2 + ≥ 0a Q∈Z}

. {QQ∈Z< T∈ +Z a Q G 2T}

I. &'-"'

. {Q∈ +Z 2Q > 0}

4E53-

&. {Q∈Z 2Q ≤ 0} 4E53-

. {Q∈` Q

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#. !ก$%&%'()*+

4.1 ก

,' (-&'&&' ( (5+# b 4E3:!3*'D3%37 , (' ",' b 4E (: ($- +$) ( ('#5+' b 3 F F

"- b 4E&'5?% *- 5 (5+!"# ,'%'4E5?%3 F

&'5 (%4E'D3%373 () /4 /-*

Z * &'5?% UZTc[d[e Y^fA[eV ,' Z G {…< −2< −1< 0< 1< 2

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" ; G &'53 (' 1

; G φ U + 1 4E53 (' ($-V

" = G {QQ 4E55 *!+ 2Q G −N}

= G φ U +/%%55- (!3'*!/- −N V

" > G {QQ 4E5?% *!+ Q G φ U +/%%5?%- (%'3%3' V

'!-,)&9 = +;!ก,!-' 7>4ก!+' 78

1. &'-4E

. {Q NQ 2 + G 0} &. {Q 0Q 2 > } . {Q 22 V1QUQ − ≤ 0} . {Q Q > I}

2. - ` *&'55 *!+ Z *5?% &'-"'

. {Q∈Z QMQI 2 − G 0} 4E

&. {Q∈Z MQ2 − ≠ 0} 4E53-

. {Q∈` Q≠ 2Q } 4E'3

.{

Q∈

`

1Q2

+ G 0}

4E'3

I. &'-/%"'

. {φ} /%4E

&. {QQ 4E5?% *!+ Q + 2 G 2} 4E

. 4E53-

. " ; 4E'3 *! ; 4E (3/%/-3 F

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5. ,)&&%()*+

5.1

; 4E3&' = ?'%, (' %$) 3&' ; 4E%&' = &*- ; ⊂ =*!+; /%4E3&' = &*- ;⊄ =

" ; G {1< 2< I}

= G {1< 2< I< M}

5+? %$3 (' ; ?4E% = -33 F ;⊂ =* %3 = ,' M /%4E% ; -33 F =⊄ ;

" > G {M< N< 6}

H G {M< 6< N}

%$3 (' > ?4E% (' H -33 F >⊂ H%$3 (' H ?4E% (' > -33 F H⊂ >

-33 F $4/- >⊂ H *!+ H⊂ >

( ; ⊂ = * = ⊄ ; ; 4E-'&' = 3 (%% 5%&' ; 5+%5'5%&' =

( >⊂ H *!+ H⊂ > !/- > /%4E3*&' H *!+ H /%4E3*&' > -

" ; G {1< 2< I}

3 (4E/4/-3 F%-&' ; ,'

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ก 1. $4E3&'3%3' 3 (,' " ; 4E-) *! ;⊂ ;

2. 4E3&'$) 3 (,' " ; 4E-) *! φ ⊂ ;

I. 53&' ; /-5 jjjjj %, (' T 4E5% ;

M. 53*&' ; /-5 jjjjj %, (' T 4E5% ;

5 ; G {2< I< M}

%&' ; /-* (4E3&' ; /-*

= G {1< {2}< 2< I} %&' = /-*

(4E3&' = /-*

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5 5&33 F%-&' ; '%3 F+$53*!+53* (4E/4/-

1. ; G {I< N< 6< O} 2. ; G {2< {I}< N}

I. ; G {1} M. ; G {−2< 0< 2}

N. ; G φ 6. ; G {φ}

O. ; G {φ< {φ}}

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'!-,)&9 = ?. +9* !,)&' 7>4ก 9* !,)&' 70

1. - ; G {1< I< N< 6}

1.1 I∈ ; 1.2 6∈ ;1.I {N} ∈ ; 1.M {I< N} ∈ ;

1.N {1< 6} ⊂ ; 1.6 φ ⊂ ;

1.O {1< I< N< 6} ∈ ; 1.S {1< I< N< 6} ⊂ ;

2.

2.1 {1< {2}} ⊂ {1< {2< M}} 2.2 2∈ {1< {2< M}}

2.I {2} ⊂ {1< {2< M}} 2.M {1} ⊂ {1< {2< M}}

2.N {2< M} ∈ {1< {2< M}} 2.6 {2< M} ⊂ {1< {2< M}}

2.O {I} ⊂ {I< 6< O} 2.S φ ⊂ φ

2.9 φ ⊂ {φ} 2.10 φ ∈ {φ}

2.11 {φ} ∈ {φ} 2.12 {φ} ⊂ {φ}

2.1I φ G {φ} 2.1M {φ} ∈ {φ< {φ}}

2.1N {φ} ⊂ {φ< {φ}} 2.16 {{φ}} ⊂ {{{φ}}< {φ}}

2.1O {φ} ⊂ {{{φ}}< {φ}}

2.1S - ; G {−M< −I

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??. +;!ก,!-' 7>4ก!+' 78

1. - ; G {1< f< {T}} &'-"'. {T} ∈ ; &. {T} ⊂ ;. φ ∈ ; . f⊂ ;

2. "- ; G {1< φ< {φ}< {1< φ}} -4E3*&' ;. {1< {1}} &. {φ< {1}} . {{φ}< {1}} . {{φ}}

I. ; G {φ< 1< {1}< 2< I< {1< 2}< {φ}< {{φ}}} 55&'%'/4 FU1V φ ⊂ ;

U2V {1< 2} ⊂ ;

UIV {1< 2}∈ ;

UMV {φ}∈ ;

UNV {{φ}} ⊂ ;U6V {2< I}∈ ;

&'-"'. "R+&' 1. 3&' N. &. "R+&' 1< 2 *!+ M. "R+&' I< N *!+&' 6. . k-R+&' 6. '3 F"%-

M. &'-"'. {2} ⊂ {0< {2}< 1}

&. {Q∈ +Z IQ2Q2 −+ G 0} G {−I< 1}

. {XX G 2Q2 < Q∈Z *!+−1 ≤ Q ≤ 0} G {−1< 0}

. {Q∈` 1QQ2 ++ G 0} G φ

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5.2 ก!ก"

; 5+3 = ?'%, (' ; *!+ = %5%3 *!+%,'3

-33 F " ; G = 5+%%%%,'3 ;⊂ = *!+ =⊂ ; 3 (' ; G {I< N< O} *!+ = G {QQ 4E55# ( UQ − IVUQ − NVUQ − OV G 0}

5+/- = G {I< N< O} -33 F ; G =

> G {1< 2< N< 9} H G {1< 2< N< 2< 9}

5+/- H G {1< 2< N< 9} -33 F > G H

'!-,)&9 = +;!ก,!-' 7>4ก!+' 78

1. - ; G {1< I< N}

= G {Q IQMQ2 +− G 0}

> G {QQ ,'5*%&'&'!l# (! (- 2 /%!3}

H G {QQ ,'53 (/-%, (': I :}

&'-". ; G = &. = G >. > G H . ; G >

2. - ; G {Q∈ +Z 2Q G 1}

= G { Q∈ −Z 2Q G 1}

> G {Q∈Z 1Q2 − G 0}

H G {Q∈` 1Q2 − G 0}

&'%'/4 F4E5 (&' 1V ; G = 2V > G H IV ; G = G > G H

. I &' &. 2 &'. 1 &' . /%%&'4E5

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I. " ;< =< > 4E- ) *! &'-/%4E5. ;⊂ ; &. φ ⊂ ;. ;⊂ φ *! ; G φ . " ;⊂ = *!+ >⊂ = *! ; G >

M. - @∈;< A∈=< ;⊂ >< =⊂ > *!+ >⊂ ; &'$4-4E?5. ; G > &. A∈>. @∈> . @∈=

5.3 ก!ก"

" ; *!+ = 4E53- 5% ; 35% = !/- ;3 =

; G {I< 6< O} = G {1< N< S}

5+? 5%&'3 F ; *!+ = 3 I 3 F !/- ; 3 =

$4 %3%37+

1. 4E3&'$) 3 (,' φ ⊂ ; %, (' ; 4E-)

2. $) 4E3&''D3%37 3 (,' ;⊂ b %, (' ; 4E-)

I. $) ?4E3&'3%3' 3 (,' ;⊂ ; %, (' ; 4E-)

M.

; G = ?'%, (' ;⊂ = *!+ =⊂ ;

N. " ; G = *! 5+/- ; *!+ = 4E (3

6. " ; *!+ = 4E (3 ; /%54E'3 =

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/. 0$%) !!!

4E*kD (&* -44m--) -3 (/45+4 (! (%k,k*'D3%37 *!+

!%*-) &D4 (! (%k,k- b G {1< 2< I< M< N}

; G {1< 2< I} = G {2< I< N}

5+&*/--*kD /-4E

# 5&*kD, ('*'/4 F

1. b G {1< 2< I< M< N< 6< O}

; G {2< M< N}

2. ; G {I< M< N}

= G {M< N< 6}

I. b G {1< 2< I< M< N< 6< O} ; G {I< M< O} = G {1< I< N< O}

M. b G {1< 2< I< M< N< 6< O} ; G {1< 2< N} = G {2< I< M} > G {1< 6< O}

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N. ; G {2< I< M< N< 9} = G {M< N< 6< O} > G {M< N< O< S< 9}

6. @ A {1< 2< I} = G {1< 2< I< M}

'!-,)&9 = +;!ก,!-' 7>4ก!+' 781. 55&'%'/4 F

U1V ; G {2< M< 6< S< 10}< = G {QQ 4E5 (' 12} -33 F ; G =

U2V " ;⊂ = * =⊄ > *! ;⊄ >

&'-"'

. U1V 3 F"'

&. U2V 3 F"'

. U1V *!+ U2V "3 F'&'

. U1V *!+ U2V k-3 F'&'

2. " ;⊂ = &'-"'

. " @∉; *! @∉=

&. " @∉= *! @∉;

. % @∈= - ( @∉;

. % @∉; - ( @∈=

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. กก''+

+ ,' '

,'$.1 %"" &'()*(+

" ; *!+ = 4E 2 @ 4

= ,'3 F&' ; *!+ = ?/- &*-

; G {1< I< N} < = G

5+/- ;∪= G

; G {2< I< N} < = G

5+/- ;∪= G

(**kD n '

,- ก ก%"" /

1. ;∪; G ;

2. ;∪= G =∪;

I. ;∪ U=∪>V G U;∪=V∪ >

M.

;∪φ G a ;∪b G

!) %+3 , ('-4E% F

B %"# (4+'-% (4E%

∪=

2< M< 6}

I< M< O}

'!' *- ;∪= 4*) -3D

*

22

# (5+%' I 7

&' ; ,'&'

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N. ;⊂ = ?'%, (' ;∪= G =

6. ;⊂ ;∪= *!+ =⊂ ;∪=

O. " =⊂ ; *!+ >⊂ ; 5+/- =∪>⊂ ;

S. " ;⊂ = *!+ ;⊂ > 5+/- ;⊂ =∪>

%3&' ( N *- (&'3+33 ,' "5- ; ⊂ = % %"$4/- ;∪= G = '-3 "5- ;∪= G = *- ;⊂ =

$ 5 ;∪= %, ('- 1. ; G {1< 2} *!+ = G {M< N< O} 2. ; G {f< T< o< p } *!+ = G {T< p< e< q< c}

I. ; G {2< I< N} *!+ = G {N< I< 2} M. ; G {M< {N}} *!+ = G {{N}< {M}}

N. ; G {I} *!+ = G {φ< {I}} 6. ; G {φ} *!+ = G {φ< {φ}}

O. ; G φ *!+ = G {φ} S. ; G {{φ}} *!+ = G {φ< {φ}}

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'!-,)&9 = +;!ก,!-' 7>4ก

1. ; G {φ< {φ}} *!+ = G { . {φ< {φ< {φ}}}

. {φ< {φ}}

ก!/0,""ก% , 6

1. 5%&' ;∪= 5+$-

2. 5%&' ;∪= 5+( $-

; G =

7 5$-*!+( $-&'

1. TU;V G N< TU=V G N

2. TU;V G I< TU=V G S

I. TU;V G O< TU=V G I

+' 78

} *! ;∪= ,'&'-&. {{φ< {φ}}} . {{φ}}

∪ ∪∪ ∪ 8

%, (' ; *!+ = /%%%-F 3!

%, (' ; G = ,' ;⊂ = ,' =⊂ ;

;⊂ = =

TU;∪=V %, ('-

2M

;

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$.2 "!-" &9(:;

" ; *!+ = 4E

*!+ = 3:!3 ;∩= ; G {1< 6< I

5+ % ('

-33 F ;∩

; G {2< {I<

-33 F ;∩ (**k

,- ก

1. ;∩; G ;

2. ;∩= G =∩;

I. U;∩=V∩ > G

M. ;∩φ G

N. ;⊂ = ?'%, ('

6. " ;⊂ = *!+

O. " ;⊂ = *!+

:)*(+

2 @ !!, B %"# (4+'-

} < = G {I< N< 6} ; *!+ = ,'

G

M}< φ< {φ}} < = G {2< {φ}< M}

G

n ''!' *- ;∩= 4*

ก"!-" /-*

∩ U=∩>V G ;∩=∩>

a ;∩b G

∩= G ;

⊂ > *! ;∩=⊂ >

⊂ > *! ;⊂ =∩>

2N

% (4E%&'3 F ;

-3D

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%3&' ( N *- (&'3+33''3 ,' "- ; ⊂ = %"$4/- ;∩= G ; '-3 "5- ;∩= G ; *- ;⊂ =

? 5&' ;∩= %, ('-1. ; G {1< 2< I< M}< = G {−2< 0< 2< M< S} 2. ; G {0< 1< 2}< = G {2< 1< 0}

I. ; G {2< I< M< N}< = G {1< S< 9} M. ; G {M< {M}}< = G {{M}< N< 6}

N. ; G {1< 2< I

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1@ - b G {0< 1< 2< I G {I< N< O< 9}

H G {1< 2< I< M< O< S< 9} 5& (-

1. ;∪= 2. ;∩=

I. ;∩> M. ;∩H

N. =∩H 6. >∩H

O. >∪H S. ;∪=∪>

9. ;∪=∪>∪H 10. ;∩=∩>∩H

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11 - ; G {1< I< M<5%%*kD*!+&*

1. ;∪=

I. =∪>

N. ;∩>

O. U;∪=V∪ >

9. U;∩=V∩ >

11. ;∩ U=∪>V

1I. ;∪ U=∩>V

1N. U;∪=V∩ >

1O. U;∩=V∪ >

< S}< = G {I< M< N< O} *!+ > G {2< I< 6< O< S !+&'

2. ;∪>

M. ;∩=

6. =∩>

S. ;∪ U=∪>V

10. ;∩ U=∩>V

12. U;∩=V∪ U;∩>V

1M. U;∪=V∩ U;∪>V

16. U;∩>V∪ U=∩>V

1S. U;∪>V∩ U=∪>V

2S

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12 - ; G {QQ 4E$&' N< 20

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'!-,)&9 = +;!ก,!-' 7>4ก

1. - ; *!+ = 4E 5

1V " ;⊂ = *! ;∩= G2V " ;⊂ = *! ;∪= G

&'-". &' 1. "*!+ &' 2. "&. &' 1. "*!+ &' 2. k-. &' 1. k-*!+ &' 2. ". &' 1.k-*!+ &' 2. k-

2. - ;⊂ = &'-k-. =∩;⊂ =

&. ;∩= ≠ φ

. ;∩= G ;

. ;∪= G =

I. " ;⊂ = - ; ≠ φ *!+ =≠ φ

. ;∩= G φ

&. ;∪= G ;

. ;∩= G =

. ;∩= G ;

M.

+' 78

&'%'/4

&'-"'

(*,'&'-. U=∪;V∩ >&. U=∩;V∪ >. =∩ U;∪>V. =∪ U;∩>V

I0

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. 02 9962692 I1

N. " ; G {Q∈` 2QIQ2 2 −− G 0 *!+ 2Q + 1 G 0} *!+ ; G {@} *! @ %/

. 2

&.21

.21

−

.21

− ,' 2

6. " ; G {−N< −I< −1< 0< 1< N< 10}< = G {−6< −I< 1< I< 6}< > G {−M< −I< −2< 1< 2< M} *! ;∩ U=∪>V 3-

. {Q∈` IQ2Q2 −+ G 0} &. {Q∈` IQ2Q2 −− G 0} . {Q∈ Y IQ2Q 2 −+ G 0} . {Q∈ Y IQ2Q 2 −− G 0}

O. - ; G {QQ 4E53 (- I !3} = G {QQ 4E5?% (- M !3}

*!+ > G {QQ 4E5?% *!+ −100 ≤ Q ≤ 100} %&' ;∩=∩> %53-

S. ; G {Q∈ZQ G 10r< r∈Z}< = G {Q∈ +Z Q G Nr< r∈Z } *! ;∩= 3&'-. ;&. =

. {Q∈ +Z Q G 10r< r∈Z}

. {Q∈ZQ G Nr< r∈Z}

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ก!/0,""ก% , 6

1. 5%&' ;∩= 5+$-

; G =

2. 5%&' ;∩ = 5+( $-

13 5$-*!+( $-&

1.

TU;V G N< TU=V G N



$.3

A-" &B)CC;;" ; *!+ = 4E 2 0*

%&' = &*- ; − = (**kD n '

8

%, (' ; G = ,' ; ⊂ = ,' =⊂ ;

;⊂ = =⊂

%, (' ; *!+ = /%%%-F 3! ,' ;∩=

TU;∩=V %, ('-

(E F*GHI;G;(:++!+ @ B ,' (4+'-%&

'!' *- ; − = 4*) -3D

I2

;

φ

; (/%4E

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; G {1< 2< I

5+? % ('

% ('

; G {2< 6< O;− = G

14 5 ; − =

1. ; G {1< 2< I< M< N}< =

2. ; G {1< 2< M< N< O}< =

I. ; G {I< N< O}< = G

M. ; G {1< 2< I}< = G

N. ; G {1< 2< M< N< O}< =

6. ; G {1< 2< {I}}< =

< M} < = G {I< M< N}

; */%' = ,' -33 F ; −

= */%' ; ,' -33 F = −

} < = G {2< 6< O< S}

!+ =− ; %, ('-; − =

G {2< M< S< 9}

G {I< 6< S}

N< I< O}

1< 2< I< M< N}

G {2< M< 6

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; 4E3&''D3%3

&' b */%4E%&' ; &*-

(**kD n '

b G {1< 2< I< M< N} < ;

5+? % (' b */%'

15 5 ;′ *!+ =′ %, ('

1. b G {1< 2< I< M}< ; G {1< 2}< =

2. b G {@< A< B< s< [< t }< ; G {@< A< B

I. b G {1< 2< I

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. 02 9962692 IN

1# - b G {0< 1< 2< I< M< N< 6< O< S< 9}

; G {0< 2< I< M< N}

= G {1< I< M< 6< O} > G {0< M< O< 9}

5&*kD*!+& (-

1. ;′ 2. =′

I. >′ M. ;∩=′

N. ; − = 6. =∩;′

O. = − ; S. ;∩>′

9. ; − > 10. U;− =V∪ U= − ;V

11. =∪> 12. ; − U=∪>V

1I. U=∪>V′ 1M. ;∩ U=∪>V′

1N. b − = 16. U;∩=V′

1O. ;′∪=′ 1S. =′ − ;′

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1$ - b G {0< 1< 2< I< M< N< 6< O< S< 9}

; G {2< M< O< 9}

= G {0< 1< M< N< 6< O}

5&% (-

1. ;∪= 2. ;∩=

I. ;′ M. =′

N. U;∪=V′ 6. ;′∩=′

O. U;∩=V′ S. ;′∪=′

9. ;− = 10. = − ;

11. b− U;∪=V 12. =′ − ;′

1I1I. 1I. ;′ − =′

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17 5**k1.

U;∪I.

U=N.

U=O.

U;∩=V9.

;∩ U

D* (-

∪>V′

2.

>V′

M.

>V′

6.

U;∩>V

S.

∪>V′

10.

U;∩=V

IO

;′∩=′∩>′

=′∪>′

=′∩>′

;∩=∩>′

∪ U;∩>V∪ U=∩>V

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11.

U;− >V∩ =1I.

U;∩=V∪ >1N.

;′∩>′∩=1O.

;′ ∩ U=∪>V

12.

;∩>∩=

1M.

>∪ U;∩

16.

U;∪=V∩

IS

V

>

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. 02 9962692

1? 5&*1.

I.

N.

O.

9.

- (**kD'/4 F2.

M.

6.

S.

10.

I9

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. 02 9962692

11.

1I.

1N.

1O.

19.

12.

1M.

16.

1S.

20.

M0

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. 02 9962692

21.

2I.

2N.

2O.

29.

22.

2M.

26.

2S.

I0.

M1

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. 02 9962692

I1.

2@ - ;⊂ b< =⊂ 1. ;⊂ =

I. >⊂ ;⊂ =

N. ;⊂ U=− >V

< >⊂ b *!+ ; ≠ = ≠ >≠ φ 5&*kD

2. ;⊂ =⊂ >

M. >⊂ ;∩=

6. U=− >V⊂ ;

M2

*'/4 F

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. 02 9962692 MI

,- ก กA-" /-*

1. ;− ; G < ;− φ G < b− ; G ;′

2. U;′V′ G

I. φ′ G *!+ b′ G

M. U;∩=V′ G < U;∪=V ′ G

N. ;∩;′ G < ;∪;′ G

6. ;− = G G

O.

;− U=− >V ≠ U;− =V − >

S. ;⊂ = ?'%, (' ; − = G φ

9. ;∩= G φ ?'%, (' ;⊂ =′

21 5&'

1. ;∪;′ 2. ;∩;′ I. ; − ;′ M. ;∪;

N. ;∩; 6. ; − ;

O. ; − U; − ;V S. ; − U;∩;V

22 " ; *!+ = /%%%-F 3! 5

1. ;∩= 2. ; − =

I. = − ; M. U;∪=V − U; − =V

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. 02 9962692 MM

23 " ;⊂ = *!+ ; ≠ = 5

1. ;∩= 2. ;∪= I. ;− =

24 - b G {0< 1< 2< I< M< N< 6< O< S< 9}

; G {I< M< N< 6}

= G {N< 6< S< 9}

5&D**!+& (-

1. ;′ 2. ;′∩=

I. ;∩ U;′∩=V M. =∪ U;′∩=V

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. 02 9962692 MN

N. =′ 6. ;∩=′

O. ;′ ∩ U;∩=′V S. =′ ∪ U;∩=′V

9. ;′∩=′ 10. ;∪ U;′∩=′V

11. ;∪b 12. ;∩b

1I. ; − = 1M. = − ;

1N. b − ; 16. b − =

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. 02 9962692 M6

25 - b G {1< 2< I G {M< N< S} 5

1.;∩

=′

2. ;∪ U=∩>′V

I. U;′∩=′V∪ >

M.;∪

U=∩

>V′

N. V>=U; ′−−

6. ;∪U=− >′V′

O.U=∩

>′V′ −

U=−

>′V′

S. =′∩ U=′ − >V

9. ;∩ U;′∩=′∩>′V

10.U;∩>′V∪ U=∩;′V

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. 02 9962692 MO

2# - ;< =< > 4E&'55 (

; G uI2

− < 2V< = G U−∞<21

− v∪ U2N

G u−I< 1V 5

1. > − U=′∩;V

2. ; − U=∪>V′

I. U>′∩=′V− ;

'!-,)&9 = ?. +9* !,)&' 7>4ก 9* !,)&' 70

1. - ; G {1< 2< I}< = G {1< 2< I< M< N} *!+ b G {1< 2< I< M< N< 6< O}

1. ;⊂ = 2. ;∪= G =

I. ;∩= G ; M. ; − = G φ

N. ;= ′⊂′ 6. ;∩;′ G φ

O. ;; ′∪ G b S. ; − ;′ G ;

9. ;′ − ; G ;′ 10. b′ G φ

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2.

1. ;− U;− ;V G ; − ;

2. ;∪; G ;∩ U;− ;V

I. ;− U;∪;V G ; − ;

M. ;− ; G ;

N. " b G {@< A< B< s< [} *!

6. " φ G ;′ *! ; G b

??. +;!ก,!-' 7>4ก!+' 78

1. - ; G {φ< {φ}} *!+. ;∩= G ;&. ;∩= G {φ}

. ; G =. ;− = G φ

2. ; G {1< 2< I< {1< 2< I}} *

. ;∩= G {{1< 2}}

&. ;∪= G {{1< 2}< {1< 2< I}

. ;− = G {{1< 2< I}< I}

. = − ; G φ

I.

+ ; G {@< B< [} *! ;′ G { A< s}

= G φ ∪ {φ} &'-"'

+ = G {1< 2< {1< 2}} &'-"

&'-/% (**kD

. ;∩=′

&. =− ;. ;′∩=

. U;∪=V − ;

MS

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. 02 9962692

M.

N.

6.

O.

S.

(*D

. U;′ − >V∪ =&. U>− ;V′ ∩ =. > ′∩ U;∩=V. ; − U=∪>V

, F ( (*4

. ;′∪=′ &. U;− =V′ ∪ =′ . U=− ;V∪ U;∩

. uU;− =V∪ =v′

(*,'&

. > − U;∪=V&. > − U=′∩;V

. ;′∩>. =′∩>

(*%"#

. U;− =V′ &. =′ − ;′ . U;− =V′ ∪ U ;′

. U;− =V∪ U;′

5*kD (*

. ; − U=∩>V&. ;∪ U=′∩>′V. U;− =V∩ U; −

. U;− =V∪ U; −

M9

%"#-

&'-

=V′

-

&'-

∪=′V

=′V′

%"#-

>V

>V

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. 02 9962692

9. - b 4E'D3%37 ;<

10. - b 4E'D3%37 ;<

11. 5*kD (- &'-4E5

12.

. M &'

. 2 &'

= 4E- ) Q 4E, F (* &'-4E5

. Q G U;∩=V∪ ;′ &. Q G U;∪=V∩ U= − ;V′ . Q G U; − =V′ ∩ U=− ;V′ . Q G U; − =V∪ U= − ;V

=< > 4E- ) *!+ Q 4E, F (* &'

. Q G U;∩=V − >

&. Q G ;∩=′∩>′

. Q G U;∪=′V− >

. Q G U; − =V∪ >′

. U;∩=V∪ UH − >V G =∩H

&. U>−

;V∩

U=′−

>V G UH∩

. U=− HV∪ U; − HV G ;∪=

. U>∩HV∪ UH − ;V G = − H

5*kD (- (*!& I (&'

1V = − {U=∩>′V∪ U;∩2V U=∩>V − U;∩=∩>V

IV U=∩;′V − U=∩;′∩>′

MV U=∩;′V − >′

&. I &'

. 1 &'

N0

4E5

V−

U;∩

=V

&'-3

∩>V}

V

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. 02 9962692

1I. &'-,' uUY∩hV nw G {@< A< B< s}< Y. {[< t< d}

&. {t< x}

. {s< d}

. {B}

1M. b G {2< I< MV′∩ = ,'

. {M< 6}

&. {I< N< O}

. {I< M< N< 6< O< S< 9

. {2< I< M< N< 6< O< S

1N. -'D3%37

> G {2< M< 6< O} *!. {6}

&. {6< S}

. {N< 6}

. {N< 6< O}

16. " ; G u1< IV< = G U2<

,'y&'-

. U;∪>V − =. U;∪=V − >

wv∪ Uw∪ Y∪hV′ %, (' b G {@< A< B< s< [< t< d<{B< s< [< t }< h G { A< s< t< d}

10}< ; G {2< M< 6}< = G {I< M< N< 6< O}< > G '-

}

< 10}

b G {1< 2< I< M< N< 6< O< S} *!+ ; G {1< 2<uU=∩>V − ;v∪ U;∪=∪>V′ ,'&'

Mv *!+ > G UI< Nv *!

&. U>∪=V − ;. U;∪>V − =′

N1

x}<

{I< N< O< 9}

I< M}< = G {I< M< N< 6}

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. 02 9962692 N2

1O. U; − =V∪ U= − ;V∪ U;∩=V 3&'-. ;∩=

&. U;′∪=′V′ . ;

. U;′∩ =′V′

1S. ;< = 4E-) 5 ;∩ U=∪;V′ 3&'-

. ;

&. =. φ

. b

19. 5 ;∩ U=− ;V 3&'-. ;

&. =. φ . b

20. 5 ; − U=∪=′V 3&'-. ;&. =

. φ . b

21. &'-!"'. ;− ; G ;&. ;− φ G φ . ;− ; G φ

. ;− ;′ G φ

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. 02 9962692 NI

22. " ; *!+ = 4E-) &'-"'

. U;− =′V⊂ ;′

&. ;′ ⊂ U;− =V′

. U;− =V′ ⊂ U=− ;V′

. U=− ;V′ ⊂ U;− =′V

2I. - ; 4E53- = 4E- ) &'-"'

. " ;⊂ = *! = 4E53-

&. ;∪= 4E53-

. ;∩= 4E53-

. ;− = 4E'3

2M. - ; G {QQ G 2T %, (' T +∈Z } *!+ = G {XX G IT %, (' T +∈Z } &'-/%"'

. ;∩= G {6< 12< 1S

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. 02 9962692

ก!/0,""ก% , 6

1. 5%&' ; − = 5+$-

2. 5%&' ; − = 5+( $-

; G =

2$ 5$-*!+( $-&'

1. TU;V G N< TU=V G N



− −− − 8

%, (' ; *!+ = /%%%-) F 3!

%, (' ; G = ,' ;⊂ = ,' =⊂ ;

;⊂ = =

TU; − =V %, ('-

NM

;

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. 02 9962692 NN

. &-' 7,% 7&&

1. ;⊂ U;∪=V *!+ =⊂ U;∪=V

2.

U;∩=V⊂ ; *!+ U;∩=V⊂ =

I. U;∩=∩>V⊂ U;∩=V

U;∩=∩>V⊂ U;∩>V

U;∩=∩>V⊂ U=∩>V

M. ;∪ U=∩>V G U;∪=V∩ U;∪>V

;∩ U=∪>V G U;∩=V∪ U;∩>VN. ;− = G ; %, (' ;∩= G φ

6. ;− U=∩>V G U; − =V∪ U;− >V

;− U=∪>V G U; − =V∩ U;− >V

O. U;∩=V − > G U; − >V∩ U=− >V

U;∪=V − > G U; − >V∪ U=− >V

27 " h *!+ i *-) *!+ i′ 4E'%!%&' i *!5&' Uh∩iV∪ Uh∩i′V

2? U;∩=∩hV∪ U;∩=∩>∩h∩iV∪ U;∩h∩=′V ,'-

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. 02 9962692 N6

'!-,)&9 = ?. +9* !,)&' 7>4ก 9* !,)&' 70

1. {@< A< B< s} *!+ { o< p< e< q} 4E/%%%

2. {O< 11< 1I} *!+ {11< 12< 1N} 4E/%%%

I. ; G = ?'%, (' ; *!+ = %%4E53

M. φ 4E3&'$)

N. " ;⊂ = *!+ =⊂ ; *! ; G =

6. " ;⊂ = *!+ =⊂ > *! ;⊂ >

O. " @∈; *!+ @∈= *! ; G =

S. " @∈; *!+ ;⊂ = *! @∈=

9. " A∈= *!+ ;⊂ = *! A∈;

10. " ;⊂ b *!+ =⊂ b *! ;− = ≠ φ

11. " ;⊂ = *! 5+/- ;− = G φ

12. " ;∪= G b *! ;′ G = *!+ =′ G ;

1I. " ;∪= G b *! ;′ G =′

1M. " ;∩= G φ *! ;′ G =′

1N. " ;∩= G φ *! ;⊂ =′

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. 02 9962692 NO

16. " ;⊂ = *! 5+/- ;= ′⊂′

1O. " ;⊂ = *!+ =⊂ > *! >′ ⊂ ;′

1S. " ; *!+ = 4E/%%% *! ;′ ⊂ =′

19. " ;∪= G b *!+ ;∩= ≠ φ *! =′ ⊂ ;′

20. U;∪=V − U;∩=V G U; − =V∪ U= − ;V

21. ;∪ U;′∩=V G ;∪=

22. ;− U;− =V G ;∩=

2I. U;∩=V∪ U;′∩=V G ;′

2M. U;∩=V ⊂ u;∪ U=∩ U= − ;VVv

2N. ;∩ U=∪>V G U;∩=V∪ U;∩>V

26. U;− =V∩ > G U;∩>V − U=∩>V

2O. ;∩ U=− >V G U;∩=V − U;∩>V

2S. ;− U=− >V G U; − =V − >

29. U;− =V∩ > G ;∩ U=′∩>V

I0. =∪ uU;∪=′V∩ U=′∪>Vv G b

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??. +;!ก,!-' 7>4ก!+' 78

1. - ;< =< >< H< J 4E-. ;&. b. =. φ

2. ;< =< >< H 4E- ) 5. ;

&. =. φ . b

I. 5 U;∩=V∪ U;∩=′V . ;

. φ

M. " ; *!+ = /%%%-

. ;∩= G ; − =

&. U;∩=V − U= − ;V G =

. U;∩=V∪ = G U;∪=V − U;

. U;∪=V − ; G ; − U;∪=V

N.

) 5 U;∪=V∪ U>∪HV∪ U;∪=′∪JV

∩ U;′∩=V∩ UU=∪>V − HV 3&'-

3&'-&. =. b

F 3! &'-"

− =V

5*kD'-!'3-

. U;∪=V∩ U;∪>′V&. U>′ ∪ U;∪=V′V′ . ;∩ U=∪>V′ . U;∩=V∪ U>∩=V

NS

3&'-

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. 02 9962692 N9

6. ;< = 4E-) 55&'%'/4 F

1V U;∩=′V∩ U;∪=V′ G φ

2V U;∩=V∪ U;′∩=V G =IV U;∩=V′ ∪ U;∪=V′ G ;′∪=′

&'-"'. "3 F &' 1. &' 2. *!+ &' I.&. "R+&' 1. 3&' 2.. "R+ &' 1. &' 3 &' I.

. "R+ &' 2. &'-

O. ;< =< > 4E-) &'%-4E'C

. ;′ − =′ G = − ;

&. ;∩ U=− >V G U;∩=V − U;∩>V

. " ;∩= G φ *! ; − = G φ

. UU;′V′V′ G ;′

S.- ;< = *!+ > 4E- ) (

′V∪ U;′∩=∩>′V∪ U;∩=′∩>V∪ U;′∩=∩>Vi G U;∪=V∩ U;∩=V′

&'->4ก . i⊄ h&. h∩i G h∪i. h∩i G φ

. i 4E3*&' h

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9. " ;⊂ =⊂ > *!+ ; ≠ =< = ≠ > &'-k-

. U;∪=∪>V∩ U;∩=V∩ U;− =V′ G ;

&. U=∩>V∪ U>− U;∪=VV G ;∪=∪>. U;′∪=V − > G U= − ;V∪ U>′− ;V

. uU;∩>V − =v′ ∩ ; G U;∩=V∪ U;∩>V

10. " ; *!+ = 4E3&''D3%37 b-'& ;+ = G U; − =V∪ U= − ;V

&'-k- . ;+ ; G φ

&. ;+ = G = + ;

. ;+ φ G ;

. ;+ = G ;∪=

11. ;< = 4E3&' b " ;∆ = G U; − =V∪ U=− ;V &'- 4ก!+ . φ ∆ φ G b∆ b

&. ;∆ =′ G U;∩=′V∪ U=∩;′V

. ;′∆ =′ G U;′∩=V∪ U=′∩;V

. ;∆ = G =∆ ;

12. - ; *!+ = 4E- ) &'-0

. ; − U;∩=V G ; − =

&. ;− =′ G ;∩=

. ;− = G U= − ;V′

. U;− =V′ G ;′∪=

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. 02 9962692 61

1I. " ;< =< > 4E- ) *! &'$4-4E'C

. u;∪ U=∩>Vv′ G ;′∩ U=′∪>′V

&. uU;∪=V′ ∪ >v′ G U;∪=V − >

. uU;∩=V∩ >′v′ G U;′∩=′V∩ >

. uU;∪=V′ ∪ ;v′ G =∩;′

". ก-8&6ก9' 7&กก'ก'+ :960$%) !!!

3@ 5'1. - b G {1< 2< I< M< N< 6< O< S}<

; G {1< 2< I< M< N}<

;∩= G {M< N}<

;∪= G b

5 =

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. 02 9962692 62

2. - ;∪=∪> G {1< 2< I− ; G {I< M}

;− = G {1< 2< 6} =− U>∪;V G {O}

>− = G {1< 2}

;∩=∩> G {N}

> ⊂ ;∪=

5 ;< = *!+ >

I. - ;∪=∪> G {0< 1< 2< I< M< N< 6< O} G b< ;∩= G {1< 2< I}< =∩> G {1< 2< 6}<

;∩> G {1< 2< N}< ;′ G {0< M< 6}< ;∪= G {1< 2< I< M< N< 6< O} 5 >

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. 02 9962692 6I

'!-,)&9 = +;!ก,!-' 7>4ก!+' 78

1. - ;− = G {1< 2< M}< = − ; G {I< N} *!+ ;∪= G {1< 2< I< M< N< 6< O} *! ;∩= 4E3&'&'-

. {0< 1< M< 6< O}

&. {0< 1< I< N< O}

. {1< 2< I< M< O}

. {1< 2< M< N< 6}

2. - ;∩= G {0< 1< 2< I}< ;∪= G {0< 1< 2< I< M< N}< ;∩> G {0< 1} G {0< 1< N} *!+ ;∪> G {0< 1< 2< I< N} ;′ − U=∩>V ,'-. {M}

&. φ . {0< 1< N}

. {M< N}

I. - b G Z< ; G {1< I< N< O< 9}< = G {2< M< 6< O}< >∩;′ G {2< M< S< 10} &'-"'

. =∩> G {2< M< 6} *!+ =∩>′ G {6< O< S}

&. =∩> G {2< M} *!+ =∩>′ G {6< O}

. =∩> G {2< M} *!+ =∩>′ G {6< O< S}

. =∩> G {2< M< 6} *!+ =∩>′ G {6< O}

M. - b G {1< 2< I< M< N< 6< O< S< 9}< 1∉;< ;∩= G {2< I}< ;∩> G {2< 6}<=∩> G {2< M< O}< ;∪=∪> G {1< 2< I< M< N< 6< O< S}< > − ; G {M< N< O} &'-k-

. ;− = G {6< S}

&. = − > G {1< I}

. ;′ ∪ U=∩>V G {1< 2< M< N< O< 9} . u;− U =∪>Vv∩ U;∩=V ≠ φ

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. 02 9962692 6N

1. %)!

%)!!+ @ %"# (4+'-%# (4E3&' ; $3 '

; &*- hU;V

; G {I< M< N}

(4E3&' ; /-*

(4E3&' ; 3 F%- %5 3

%, ('! F/4 (4E%&' &/-4E

F '&' ;

= G {I< {M}}

(4E3&' = /-*

(4E3&' = 3 F%- %5 3

-33 F hU=V G

∴5%'&' ; ?,' 533 F%-&' ; 3 (' # (/-5T2 %, (' T 4E5% ;

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. 02 9962692 66

31 5&'&' (- '%3 F+$5%&' *!+5%&''

&' '5

%&'

5%&''

1. {M}

2. {I< O}

I. {2< {6}< S}

M. {N< {{N}}}

N. {φ}

6. φ

O. {{φ< {φ}}}

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&' '5

%&'

5%&''

S. hUφV

9. {{φ}}

10. {1< {1< 2< I

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. 02 9962692 6S

'!-,)&9 = +9* !,)&' 7>4ก 9* !,)&' 70

1. - ; G { φ< 0< 2< M< {φ}< {0}< {0< 2}}

1.1 φ ∈ hU;V

1.2 {φ} ⊂ hU;V

1.I {φ} ∈ hU;V

1.M {{φ}} ∈ hU;V

1.N {0< 2} ∈ hU;V

1.6 {0< 2} ⊂ hU;V

1.O {{φ}< 2} ∈ hU;V

1.S {{φ}< 2} ⊂ hU;V

2.

2.1 {N} ∈ {{N}} 2.2 φ G {}

2.I {N} ⊂ {{N}} 2.M φ G {φ}

2.N φ ⊂ {I< M

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. 02 9962692 69

-33 F 5%&'' ; ?,' 533 F%-&' ; 3 (' %"$4%33:&''/--3 F

1.

hUφV G {φ} 2. hU;V ≠ φ 3$) &' ;

I. φ ∈ hU;V

M. φ ⊂ hU;V

N. ; ∈ hU;V

6. {;} ⊂ hU;V

O. {φ} ⊂ hU;V

S. " ; 4E'3*! hU;V 5+4E'3

9. " ; %5%3 T *! 5%&' hU;V 3 T2 *!+53*

&' ; G T2 − 1

10. ;⊂

= ?'%, (' hU;V⊂

hU=V

11. hU;V∩ hU=V G hU;∩=V

12. hU;V∪ hU=V ⊂ hU;∪=V

32 5'

1. - ; G {1< 2} < = G {2< I} 5

1. hU;V∩ hU=V

2. hU;∩=V

I. hU;V∪ hU=V

M. hU;∪=V

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2. - ; G {1< 2} < = G {I< M} 5

1. hU;V∩ hU=V

2. hU;∩=V

I. hU;V∪ hU=V

M. hU;∪=V

I. - b G {2< I< M< N< 6< O< S< 9}< ; G {N< 6< O}< = G {6< O< S< 9} *!+ > G {2< I< M< N} 5

1. hU;V∩ hU=V

2. hU;V∩ hU>V

I. hU;′V∩ hU=′V

M. hU>− ;V∩ hU>− =V

N. hU;V∩ hU=′V∩ hU>V

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. 02 9962692 O1

'!-,)&9 = ?. +9* !,)&' 7>4ก 9* !,)&' 70

1. φ ∩ ;∈ hU;V

2. " ;⊂ = *! hU;V∩ hU=V G hU;V

I. " hU;∪=V G {φ} *! ;∪= '5/%3 φ

M. hU;∪=V G hU;V∪ hU=V

N. " ;≠ φ *! ;⊄ hU;V

6. {{2< I}} ∈ hU{N< {2< I}}V

O. {I< N} ∈ hU{{I< N}}V

S. " @∈; *!+ A∈= *! {{@}< {@< A}} ⊂ hU;∪=V

9. " @∈; *!+ A∈= *! {{@}< {@< A}} ∈ hUhU;∪=VV

??. +;!ก,!-' 7>4ก!+' 78

1. - ; G {1< {1}< {2}< 2} &'-/%"'

. {1} ∈ hU;V &. φ ∈ hU;V. {1< 2}∈ hU;V . {φ< {1}} ∈ hU;V

2. 3 ; -) &'%&'-DE'C

. ;∈ hU;V &. {;}∈ hU;V

. φ ∈ hU;V . φ ⊂ hU;V

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. 02 9962692 O2

I. ; 4E- ) &'-"'

. ; 4E3&' hU;V

&. ; 4E3*&' hU;V

. φ 4E3*&' ;

. φ 4E3*&' hU;V

M. " ; G {1< 2< {I< M}< {N< 6< {O< S}< 9}} *! TUhU;VV 3&'-

. M &. 16. I2 . 12S

N. - hU;V G {φ< {1}< {{1}}< {1< {1}}} &' TUhU;V − ;V %3&'-. 16&. M

. S. I

6. " ; G {1< 2< I< M< N} *!+ = G {M< N< 6< O} *! uhU;V− hU=Vv %5%3&'-. 16&. 1O. 2S

. 29

O. &'-4E?5

. U;∩=V∈ hU;V∩ hU=V

&. U;− =V∈ hU;∪=V

. U;∪=V∈ hU;V∪ hU=V

. % ;∈= *!+ ;⊂ =

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. 02 9962692 OI

S. - ; G {φ< 2< {2}}

= G {φ< {2}< {I}}

> G {φ< {2}< {{I}}} hU;V∩ hU=V∩ hU>V %3&'-

. {φ< {φ}< {{2}}} &. {φ< {{φ}}< {φ}< {2}}

. {φ< {φ}< {{2}}< {φ

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. 02 9962692 OM

12. -'D3%37 b G {1< 2< I< M

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. 02 9962692 ON

11. ก)&6ก!+

5%&' /- 2 7 ,'

11.1 JA" "" K !-!!

1.1 (!"#$4E3&''D3%37 b %'1.2 ; 4E) # ( *!+ Q 4E%-) 'D3%37

"- Q∉; *- Q∈;′

"- Q∉;′ *- Q∈;

33 5*kD n ''!' +$5%*!+ %, ('-1. TUbV G 100<

TU;V G M0<

TU=V G 2N<

TU;∩=V G 6

2. TUbV G N0< TU;V G 2N<

TU=V G 20< TU;∩=V G 12<TU;∩>V G 1N< TU=∩>V G 10<

TU;∩=∩>V G N TU;∪=∪>V G TUbV

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. 02 9962692 O6

34 5'

1. - TUbV G 100< TU;∪=V G N0< TU;V G M0< TU=V G I0 5

1. TU;∩=V 2. TU;− =V

I. TuU;∪=V′v M. TuU;∩=V′v

2. - ;< = 4E3&' b *!+ TUbV G 100 - ( TU;∪=V G M0< TU;V G I0 *!+ TuU; − =V′v G 90

5

1. TU;∩=V 2. TuU;∩=V′v

I. TuU;∪=V′v M. TU=− ;V

N. TU=′ − ;′V

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. 02 9962692 OO

I. ;< = *!+ > 4E3&' b - ( TUbV G 200< TU;∩=∩>V G N< TU;∩=V G O< TU;∩>V G 6<TU=∩>V G S< TuU;∪=∪>V′v G 60< TU;′V G 1M0< TU=′V G 1N0 5

1. TU>V 2. TU;∪=∪>V

I. Tu;− U=∪>V′v′ M. Tu;′ ∪ U=∪>V′v

N. TuU;∪=V′ ∪ U=∪>V′v 6. TuU;∩>′V∪ U=∩>′Vv

O. Tu>′ ∪ UU;∪=V − >V′v S. TuU;∩=V′ − >v

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. 02 9962692 OS

35 5'1. 3 1

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. 02 9962692 O9

M. 3'# (%3 F%- S0 %3 M0 (/%'-< 1N 'K*/%'- 553 ('-,'K

N. 555 200 (3%'34+F 4!* 3F 4!k% $ ('F 4!k%5+'F 4!* % (/%'F 4!k%5 S0 *!+/%'F 4!*5 M0 55 ('34+F 4!*'-

6. #5 N00 (3%'34+% I 4+D ,' / !*!+3 ( %'!*!+/ M0 '!*!+3 ( I0 /%'! I00

- (k ('/ 5+/%'3 ( 55 ('!'-

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. 02 9962692 S0

O. 5'"%3 100 (3%'!K % I1 '!'!21 '!y$'! M6 '!4m4' 11 '!'!*!+y$'! 9 '!y$'!*!+4m4' 10 '!4m4'*!+'! *!+% 6 ('!K3 F I -

%3 (/%'!K3 F%- (

S. 5'"%%', F'3 2 - &'*# ( 5 100 5 F%k M0 %k '/ 20 *!+'%*/%'/ 10 k :'/ I0 '% 2N *!+/%'33 F'- 10 55k : ('/*!+%

9. 5%%&'3 1N0 (%''&'4+33{ -4E3 60 3 (%3{5+%4+- %3: (/%%3{ I0 %3 (%3{ 10 *!+%3 (/%%4+ 20 5

1. 53 (%4+-

2. 53: (%4+*!+3{

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. 02 9962692 S1

'!-,)&9 = +;!ก,!-' 7>4ก!+' 78

1. "- b< ;< = *!+ ;∩= %5% 200< 100< N0 *!+ 2N %!-35%&' =− ; % (%. 2N

&. N0

. ON

. 12N

2. " ; *!+ = 4E (%5%3 - TU;∩=V G 2 *!+ TU;∪=V G 10 *!&'-4E5%&' =− ;. I 3&. M 3. N 3. 6 3

I. k!5&'533- ) # (4+4E' 1

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. 02 9962692 S2

N. 3!$ %# (5 19 % 9 * % 1M K % 12 * % M K'- 1 *'- N **!+K 2 3 F*< * *!+K -3*!+!$ % F5+&''' 1 ( I ( F

5%-? ( (R+**!+K ,'R+**!+K ,'R+**!+*. S &. 11 . 12 . 1M

6. 3%D*% 11S (k3y''' 1 (' 5% (''/4 F 60 N2 *y~ M6 4 "%*% S *!+*y~*/%4 12 *!+4*/%*y~ 6 3 F% (' F 5+%*% (3 Fk3y'*y~*!+4*/% (. S

&. 10 . 12 . 1S

O. 5'"%3 120 'K I 4+D'/4 F,'/% %'y$'! 6S

''! MM ''!!'! IO "%''!*!+'!!'! O 'y$'!*!+'!*/%''!!'! 1M 'y$'!'- IN 5+% (/%'K3 F%- F (. S &. 11 . 1I . 1N

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. 02 9962692 SI

S. 3'# (% MS ' D'38 *!+ D/ 4•k!-3 F%3 '/- 20

'/-D'38 1N

'/-D/ 2N '/-'- 10 '3 F% I

3 ('/-3 FD/ *!+D'38 % (

9. *# (%3 600 3: N00 5 F4E3533- I00 4E3K N0 3533- 200 3K I0 3533- (4E3K 2N # (5 F4E 1N "%3:# (%53-*!+/%4E3K% (. 21N &. ISN . 90 . 110

10. ;< = *!+ > 4E *!+ b G ;∪=∪>" ;∩=< ;∩>< =∩>< ;∩=∩> *!+ b %5%3 S< 9< 10< I *!+ MN %!-3k!&'5%&' ; − U=∪>V< =− U;∪>V *!+ > − U=∪;V ,'&'-. 2M&. 2I

. 22. 21

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. 02 9962692 SM

11. - TUbV G 1N0< TU;∩=V G N0< TU>V G 10< TU;V G O0< TU=V G S0 *!+ > ⊂ U;∩=V5 TU;∩=′V+ TU=− ;V+ TU;∪=∪>V′ . N0&. O0. 100. 1I0

12. " ; *!+ = 4E-) # ( TUhU;VV G I2< TUhU=VV G S *!+ TUhU;∪=VV G 6M *!TU; − =V 3&'-. M&. I. 2. 1

11.2 J%! -3 F%, ('- b 4E'D3%37 ;< = *!+ > 4E53- # (?4E3&''D3%37 b

1. " ;∩= G φ *! TU;∪=V G TU;V + TU=V

2. " ;∩= ≠ φ *! TU;∪=V G TU;V + TU=V − TU;∩=V

I. TU;∪=∪>V G TU;V+ TU=V + TU>V − TU;∩=V − TU;∩>V − TU=∩>V + TU;∩=∩>V

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. 02 9962692 SN

3# 5'1. 53%D33 F%37%#4C ( 6 5 110 &'*# ( (3K (3

' 4•k!-3 F'y$'! 2N ''! MN ''!!'! MS 'y$'!*!+'! 6 'y$'!*!+'!!'! 10 ''!*!+'!!'! S /%'K4+D-!%4+D F 11

53 ('K3 F%4+D

2. 33 F%37%4!&'*# ( % OMS *!+5+'4E%&'%%'' 1%% I %% "%3 IMS /%/-4E%%%$7 %3 IIS /%4E%&'%%D %3 I12 /%4E%&'%% %3 20M 4E%3 F%%D*!+%% %3 210 4E%3 F%%$7*!+%% %3 196 4E%3 F%%$7*!+%%D 5

1. %3 ( (4E%3 F%%% F

2. %3 ( (4E%&'%%$7%%-

I. %3 ( (4E%%%D*!+%%$7 */%4E%%%

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. 02 9962692 S6

'!-,)&9 = +;!ก,!-' 7>4ก!+' 78

1. 5'"%3'$!*# (5 ON % IO ' II '*% M0 '$3& 16 '3 F*!+*% 11 '3 F*%*!+$3& 12 '3 F*!+$3& /%%3'$!/! (!-33 F%- F 553 ('33 F%-. I &. M . N . 6

2. 3'# (%5 N0 /434+'!3%3 -%'!,'34+/-I ' ,' &*/< &%4€*!+%%+!+' 4•

S !,'34+&*/3&%4€ 10 34+%3&%4€O 34+&*/3% 2I 34+&*2N 34+&%4€ 22 34+%*!+% 2 /%34+3 F%'

5%3 (34+&*'- (

I. k!53 1

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. 02 9962692 SO

M. 4+$%3 F# (%k &%4+$% OMN "%k ('''!'- S '3 F''*'&' / 5,': (4$ | ''# (-*!+%k ''*' I - F3 F* 2 - F/4 5 9N ''/*!+: (4$ |

5 NM ''/*!+55 M6 ''5*!+: (4$ |5 IN "k (''*'/%'': (4$ |!5 2OO 5+% ( ('': (4$ |'-. IN &. NM . I91 . M01

N. - ; *!+ = 4E53- " TUV %"# 5%&' %, (' 4E-) *!&'$4-/%"'

. TU;∪=V + TU;∩=V G TU;V + TU=V

&. TU;∩=′V + TU=V G TU;∪=V

. TU;− =V G TU;V − TU=V. TU;∩=′V + TU;∩=V G TU;V

6. + (/43' (+!*# (%‚ 1I 3 " ‚' ''*5%*"3/‚'''?*5%%' "+ (3'' 3 F%'

*5%' 11 3 *!+''*5% 12 3 "%/43'% (3. 1M&. 1N. 16. 1S

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. 02 9962692 SS

--FGก'-'

?. +9* !,)&' 7>4ก 9* !,)&' 70

1. ; G {Q∈Z 2QIQ22

−− G 0} 4E (%% 2 3

2. {{2< N}} ⊂ {2< N}

I. " ;∩= 4E53-*! =∩ U;∪=V 4E53-

M. '3 ∩ '3 G '3

N. " ;∩= G ;∪= *! = G ;

6. " ;− =′ G φ *! ; G = G φ

O. " ;∪= G φ *! ;′⊂ =

S. " ;∩= ≠ φ *! ;≠ φ

9. " ;∩= G ;∩> *! 5+/- = G >

10. " ;∈= *!+ =∈> *! 5+/- ;∈>

11. " ;⊄ = *!+ =⊄ > *! 5+/- ;⊄ >

12. " ;∪= G = *!+ ; ≠ = *! ;= ′⊂′

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. 02 9962692 S9

??. +;!ก,!-' 7>4ก!+' 78

1. ; G {Q" Q∈; *! Q⊂ ;} &'-& ; **5*5%/%"'

. ; G {φ} &. ; G {φ< {φ}}

. ; G {{φ}< {{φ}}}

. ; G {φ< {φ}

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. 02 9962692 90

N. " ;∩= G ;∪= *! &'-"'. ;∩= G φ

&. ; G φ . ;− U;∩=V G =

. ;∩= G ;

6. &'- 4ก!+ %, (' ;< = *!+ > 4E- )

. ;∩= ⊂ ;− =

&. U;− =V′ G ;′ ∪ U;∩=V. ;∩= G =∩> *! =∩>⊂ ;

. ;∪b′ G φ *! hU;V G {φ}

O. - ; G {{I< M}< {N< 6}< {O< S}} &'-"'

. {I< M} ∪ {N< 6} ∪ {O< S} G ;

&. TUhU;VV % 62 5

. {I< M} ∪ {N< 6} ⊂ ;

. {I< M< N} ∩ {2< I< M< 6}∈ ;

S. b 4E'D3%37 *!+{0< 1} ⊂ b" U@< AV G {{@}< {@< A}} 3$ ) % @< A-) &' b *!5& U0< 1V∩ U1< 0V **5*5%

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. 02 9962692 91

9. - ; *!+ = 4E-) 55&'%'/4 F

1V " ;⊂ = *! =′⊂ ;′

2V " ;⊂ = *! U;∪=V − U;∩=V G = − ;&'-"'. &' 1." *!+ &' 2. "&. &' 1." *!+ &' 2. k-. &' 1. k- *!+ &' 2. ". &' 1.k- *!+ &' 2. k-

10. " ; *!+ = 4E53- &'-"'

. 5%&' ;∪= 3k!&'5%&' ; *!+ =

&. 5%&' ; − = '5%&' ;

. " ; G {s} *!+ = G hU;V *! {{s}}∈ hU=V. U;∪=V ⊂ {;< =}

11. &'-"

. " ; 4E-) *! ;⊂ hU;V&. " ; *!+ = 4E-) *! U;∩=′V∩ U; − =′V 4E

. " ; *!+ = 4E-) # ( ;⊂ = *! =⊄ ;

. " ;< = *!+ > 4E- ) # ( ;∩> G =∩> *! ; G =

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. 02 9962692 92

12. 55&'%'/4 F

U1V " U;∩>V∪ U=∩>′V G φ *! =⊂ >⊂ ;′

U2V uU=′ − ;V∪ >v∩ ; G ;∩=UIV " hU;V *'&' ; 5+/- hUhU;V V %5% 1 3 %, (' ; G φ

&'-"'. &' 1 n I "$&'&. "R+&' 1.. "R+&' 1. *!+ &' I.

. "R+&' 2. *!+&' I.

1I. " ;< = *!+ > 4E-) &'% ("','&'-

. " ;∩= G >∩= *! ; G >

&. " ;∪= G >∪= *! ; G >

. " U;∪=V′ ⊂ U>∪=V′ *! ;⊂ >

. " ;∩= ≠ φ *! ;≠ φ

1M. ; *!+ = 4E-) &'-k-

. " ;⊂ = *! ;∪ U=− ;V G =

&. " ;⊂ = *! ;∩=′ G φ

. " ;∩= G φ *! ;∪=′ G =′ . " ;∩= G = *! uU;∩=V∪ =v′ G ;− =

1N. " ;∪= G φ &'-0

. ; G = G φ &. ;⊂ =

. ;⊂ =′ . ;′ ⊂ =

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. 02 9962692 9I

16. &'-"'

. " ;− = G ; *! = G φ

&. " ;∪= G = *! = − ; ≠ φ . " ;∪= G ;∩= *! ; G = G φ

. " ;∩= G = *!+ ;⊂ = *! ; G =

1O. ;< = *!+ > 4E- ) 55&'%'/4 F

U1V

U;∩>V − U=∪HV G U; − =V∩ UH− >VU2V U;∪=V − > G U; − >V∪ U=− >V

&'-"'. "3 F&' 1. *!+ &' 2.&. "R+&' 1.. "R+ &' 2.. k-3 F&' 1. *!+ &' 2.

1S. ;< = *!+ > 4E - ( ;⊂ = *!+ ;⊂ > &'-"'

. ; G =∩>

&. U=− >V∪ ;∪ U> − =V G =∪>

. =⊂ > ,' >⊂ =

. U=∩>V∪ ; G =∩>

19. " =′∩;′ G φ *!+ ;∩= G φ &'-0

. ;⊂ =′

&. ;∩=′ G ;

. ;∪=′ G =′

. ; G = G φ

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. 02 9962692 9M

20. - ; 4E'3 *!+ = 4E-) &'-"'

. " =⊂ ; *! = 4E53-

&. ;∪= 4E'3. ;− = 4E'3

. k-$&'

21. " ;⊂ = 55&''/4 F

1V ;∪= G = 2V ;∩= G ; IV TU=′V ≤ TU;′V

MV =− ; G ; − = NV ; − = G ;∩=′ &'-"'

. " N &' &. " M &'

. k- N &' . k- I &'

22." ;∩= G φ *! &'-"'. ; G = G φ

&. ;⊂ =

. ;⊂ =′

. ;′ ⊂ =

2I. &'-4E5

. " ;≠ = *!+ = ≠ > *! ;≠ >

&. " ;∈= *!+ =∈> *! ;∈>

. " ;∪=≠ φ *! ;≠ φ

. " ;∩=≠ φ *! ;≠ φ

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. 02 9962692 9N

2M. " ;− = G = − ; *! &'$4-/%+ . ;∩= G ;&. ;∪= G =. U=− ;V∪ ; G ;. ; G = G φ

2N. &'%'/4 F4E5 (&'

1V " ;⊂ = *! ;∪ U= − ;V G =

2V " ;∩> G =∩> *! >− ; G > − =

IV " ;∩= G φ *! ;⊂ =′

MV " >∩H G φ *! >′ ⊂ H

. 1 &'&. 2 &'. I &'

. M &'

26. &'-"'

. " ;< = 4E'3 *! ;∩= 4E'3

&. " ;< = 4E'3 *! ;− = 4E'3

. " ; 4E'3 *!+ = 4E53- *! ;− = 4E53-

. " ; 4E'3 *!+ = 4E53- *! =− ; 4E53-

2O. "33 F%-&' ,' φ< {{1}} *!+ {2} *!+ ƒ G {1< {2}} *! ∩ƒ ,'&'-. φ &. {1} . {2} . {1< 2}

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2S. - ; „ = G {∈; ,' ∈= * ∉;∩=} &'-k-

. ; „ = G U; − =V∪ U=− ;V

&. " U;− =′V G φ *! ; „ = G ;∪=. " U;− =V G φ *! ; „ = G = − ;

. U; „ =V∩ ; ≠ ;− =

29. 55&'%'/4 F

U1V " ;⊄ = *!+ =⊄ > *! ;⊄ >

U2V " ;⊂ = *! ;⊄ U;∩=V

UIV " ;∩= ≠ φ< =∩> ≠ φ *!+ ;∩> ≠ φ *! ;∩=∩> ≠ φ

&'-"'

. &' 1 n I "$&'&. "R+&' 1. *!+ 2.. "R+&' 1. *!+&' I.. k-$&'

I0. 55&'%'/4 FU1V " ;∉= *!+ =∉> *! ;∉>

U2V " ;∈= *!+ =∈> *! ;∈>

UIV " ;≠ = *!+ =≠ > *! ;≠ >

&'-"'. &' 1 n I "3 F I &' &. "R+&' 1.*!+ &' 2.

. "R+&' 1.*!+&' I. . k-$&'

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I1. "- Z *&'5?%*!+4E'D3%37 ;< = *!+ > 4E3&' Z- ( ; G {Q1 ≤ Q ≤ M}< = G {Q−I ≤ Q ≤ M}< > G {−I< −2< 0< 1} 5&'-"

. ;∪> G =&. U=− ;V∩ > G {−I< −2< 0}

. U;∪=V∩ U;∪>V G ;∪=

. >′ G {QQ

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IM. &'-k-

. φ ⊂ {φ}

&. φ ∈ {φ} . {φ} ⊂ h({φ})

. hUφV G hU{φ}V

IN. - ; G {@< {@}< A< { A}< {@< A}} 55&'%'/4 F

U1V {@}< { A} *!+ {@< A} 4E%&' ;

U2V {@}< { A} *!+ {@< A} 4E3&' ;

UIV " = 4E3*&' ; *! 5%&' = 5+%' ($-3

UMV " H 4E3&'* ; *! 5%&' hUHV % ($-3 2 I1

&'$4-"'

. " 1 &'&. " 2 &'. " I &'. "3 F M &'

I6. " b ,' 'D3%37 (%% M0 3 5%&' hU;V *!+ hU=V %!-3 ,' I2 *!+ S55 (% ($- (5+4E/4/-&' ;∪=< ;∩=< ; − =< = − ; %!-3,'&'-. S< N< N< I&. S< I< N< I. O< 2< N< 2. O< N< 2< 2

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IO. - TUhUhU;VVV G 16 *!+ TUhUhU=VVV G 2N6 55&'%'/4 F

U1V I ≤ TU;∪=V ≤ N

U2V 0 ≤ TU;∩=V ≤ 2UIV 1 ≤ TU;′∩=V ≤ I

&'$4-"'. " 1 &' &. " 2 &'. "3 F I &' . k-3 F I &'

IS. ;< = *!+ > 4E-) &'%-"

. " ; 4E *! '&' ; 4E

&. U;∩=V⊂ ; − =

. hU;∪=V G hU;V∪ hU=V

. U;− =V′ G ;′ ∪ U;∩=V

I9. - ;< = *!+ > 4E/% *!+ hUV 4E'&' %, (' 4E-)55&'%'/4 F

1 V uU;− =V − >v∈ hUV %, (' G ;∪=2V U; − =V∈ hUV %, (' G U=′∪>V∩ ;

&'%&4E5,'?5. &' 1. *!+ &' 2. 4E5 &. &' 1. 4E5 &' 2. 4E?5. &' 1. 4E?5 &' 2. 4E5 . &' 1. *!+ &' 2. 4E?5

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M0. &'- 4ก!

. {Q∈ZQ

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