berbagai macam Himpunan

8/18/2019 berbagai macam Himpunan

1/10

KUMPULAN SOAL TENTANG HIMPUNAN

S = { bilangan asli },

A = { bilangan ganjil }

B = { bilangan prima ! },

Himp"nan #i a$as #apa$ #in%a$a&an #alam #iagram '(nn b(ri&"$ )

B*

+* *

P(mba-asan

S = { ., !, /, 0, 1, * * * }

A = { ., /, 1, 2, .., * * * }

B= { /, 1, 2, .., * * * }

Kar(na s(m"a angg3$a -imp"nan B #i m"a$ #i A , ma&a B ⊂ A, ar$in%a &"r'a B a#a #alam &"r'a

A*

4a#i ja5aban %ang b(nar a#ala- ) +

P(r-a$i&an #iagram 6(nn b(ri&"$7

P 8 9 a#ala- :*

A* {.,!,/,:,;}

B* {.,!,/,0,1,


2/10

4i&a K = { &, 3, m, p, a, s } #an L = { m, a, s, ", & }, ma&a K ∪ L =* * *

{ p, 3, s, ", &, m, a } +* { p, a, &, ", m, i, s }

{ m, a, s, b, ", & } * { &, a, m, p, ", s }

P(mba-asan

K = { &, 3, m, p, a, s }

L = { m, a, s, ", & }

K ∪ L = { &, 3, m, p, a, s, " }

ian$ara ja5aban A, B, +, #an %ang m(mili&i angg3$a K = angg3$a K ∪ L a#ala- 3psi A

K"n>i ja5aban ) A

4i&a P = { ?a&$3r #ari .@ }

9 = { $iga bilangan prima p(r$ama }

Ma&a P ∪ 9 = * * *

{ ., !, /, 0, 1, 2, .@ }

{ ., !, /, 0, 1, .@ }{ ., !, /, 0, 1, 2, .@ }

{ ., !, /, 1, .@ }

P(mba-asan

P = { ., !, 1, .@ }

9 = { !, /, 1 },

Ma&a )

P∪ 9 = { ., !, /, 1, .@ }

K"n>i 4a5aban) A

ib(ri&an P = { ., !, /, , .!, ./ }* Himp"nan &(lipa$an / %ang $(r#apa$ #i P a#ala- :{ } +* { /, .! }

{ /, } * { /, i 4a5aban) +

i&($a-"i { .1, 0, 2,


3/10

!, 0, #an ang&a i 4a5aban) A

4i&a A = { @, . } ma&a n A =:

@ B* . +* ! * /

P(mba-asan

N A a#ala- simb3l #ari &ar#inali$as a$a" ban%a&n%a angg3$a s"a$" -imp"nan* 4a#i ban%a&n%a

angg3$a s"a$" -imp"nan #ari -imp"nan A a#ala- !, %ai$" @ #an .*

K"n>i 4a5aban) A

A⊂ B #(ngan n A = .. #an n B = .; ma&a n A 8 B = * * *

2 +* ..

.; * !;

P(mba-asan

n A = ..

n B = .;s($iap A⊂ B ma&a A 8 B = A

s(-ingga n A 8 B = n A

n A 8 B = ..

K"n>i 4a5aban) B

iagram 6(nn #iba5a- ini m(n"nj"&&an ban%a& sis5a %ang m(ngi&"$i (&s$ra &"ri&"l(r bas&($

#an '3li #alam s(b"a- &(las* Ban%a& sis5a %ang $i#a& g(mar bas&($ a#ala- * * *

.! 3rang

.1 3rang

. 3rang!! 3rang

P(mba-asan

Ban%a& sis5a %ang $i#a& g(mar bas&($ #i$"nj"&&an 3l(- #a(ra- arsiran pa#a #iagram 6(nn* ang

$i#a& g(mar bas&($ = .! F 2 = .

K"n>i 4a5aban) +

ari s"a$" &(las $(r#apa$ !1 sis5a s"&a m(mba>a, /@ 3rang s"&a m(ngarang* 4i&a .! 3rang s"&a

m(mba>a #an m(ngarang, ban%a& sis5a #alam &(las $(rs(b"$ a#ala- :


4/10

ja#i, ban%a& sis5a #alam &(las a#ala- 0/ 3rang*

4a5aban +

alam s(b"a- &(las $(r#apa$ .2 3rang sis5a g(mar ma$(ma$i&a, .1 sis5a g(mar ?isi&a, ; sis5a

g(mar &(#"an%a* Ban%a& sis5a #alam &(las a#ala- * * *

.< sis5a

!0 sis5a

/! sis5a

0@ sis5a

P(mba-asan

n M = .2 3rang

n = .1 O3rang

n M 8 = ; 3rang

n M ∪ = n M F n n M 8

= .2 F .1 ;

= /! ;= !0 3rang

4a5aban B

alam s(l(&si p(n(rimaan sis5a, s($iap sis5a -ar"s l"l"s $(s ma$(ma$i&a #an ba-asa* ari .;@

p(s(r$a $(r#apa$ .@/ 3rang #in%a$a&an l"l"s $(s ma$(ma$i&a #an .0! 3rang l"l"s $(s ba-asa*

Ban%a& sis5a %ang l"l"s s(bagai p(n(rima b(asis5a a#a ** *

/; 3rang +*


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Bi3la #an Gi$ar = .@ 3rang*

4"mla- sis5a #i &(las = 0@ 3rang*

4"mla- sis5a = n B F n G n B 8 G

0@ D = .! F /! .@

0@ D = 00 .@

= 0@ /0 = <

4a5aban +

4i&a -imp"nan B⊂ A #(ngan n A = !1 #an n B = .2, ma&a n A∪ B = * * *

;

..

.2

!1

P(mba-asan

n A = !1n B = .2

s($iap B⊂ A ,

ma&a A∪ B = A

s(-ingga n A∪ B = n A

n A∪ B = !1

ja5aban

alam &(las $(r#apa$ !@ sis5a g(mar ma$(ma$i&a, .1 sis5a g(mar ?isi&a, ; sis5a g(mar

&(#"an%a* Ban%a& sis5a #i#alam &(las a#ala- * * * *

!/ sis5a

!2 sis5a!; sis5a

0/ sis5a

P(mba-asan

n M = !@ 3rang

n = .1 3rang

n M 8 = ; 3rang

n M ∪ = n M F n n M 8

= !@ F .1 ;

= /1 ;

= !2 3rang

4a5aban B

S(b"a- ag(n p(nj"alan majala- #an &3ran ingin m(mili&i p(langgan s(ban%a& 21 3rang* Ban%a&

p(langgan %ang a#a saa$ ini a#ala- s(bagai b(ri&"$ ) !@ 3rang b(rlangganan majala-, /1 3rang

b(rlangganan &3ran, #an 1 3rang b(rlangganan &(#"an%a* Agar &(inginann%a $(r>apai, ban%a&

p(langgan %ang -ar"s #i$amba-&an a#ala- * * *

.@ 3rang


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.1 3rang

!1 3rang

2@ 3rang

P(mba-asan

Misal ) %ang b(rlangganan majala- a#ala- A, #an %ang b(rlangganan &3ran a#ala- B, ma&a )

n S = n A F n B n A 8 B F n A ∪ >

21 = !@ F /1 1 F n A∪ B >

21 = 1@ F n A ∪ B >

n A∪ B > = 21 1@

n A∪ B > = !1

ja#i, ban%a& p(langgan %ang -ar"s #i$amba-&an a#ala- !1 3rang*

4a5aban +

ari .0/ sis5a, 1 sis5a s(nang ma$(ma$i&a, ;2 sis5a s(nang ?isi&a,


7/10

K"mp"lan p(n%a&i$ %ang #i #(ri$a man"sia

P(mba-asan

K"mp"an plan($ #alam $a$a s"r%a

K(angg3$aann%a #apa$ #i$(n$"&an #(ngan j(las, ma&a &"mp"lan nama plan($ #alam $a$a s"r%a

m(r"pa&an -imp"nan*

K"mp"lan -(5an b(r&a&i (mpa$

K(angg3$aann%a j(las #an ini m(r"pa&an -imp"nan*

K"mp"lan ma&anan %ang manis

K(angg3$aann%a #apa #i$(n$"&an #(ngan j(las %ai$" ma&anan %ang b(rasa manis s(p(r$i &"( $ar$,

&"( b3l", #3#3l, #an p(rm(n* Ini a#ala- -imp"nan*

K"mp"lan ib"&3$a pr3'insi #i P"la" S"ma$(ra

K(angg3$aann%a #apa$ #i$(n$"&an #(ngan j(las, ma&a &"mp"an ib"&3$a pr3'insi #i P"la"

S"ma$(ra m(r"pa&an -imp"nan*

K"mp"lan ma&anan %ang l(Ja$

P(ng(r$ian l(Ja$ $i#a& j(las ba$asn%a, misaln%a rasa pa-i$, asam, manis, asin * (ngan#(mi&ian, &"mp"lan ma&anan %ang l(Ja$ b"&an -imp"nan*

K"mp"lan ana& %ang b(r&"li$ g(lap

arna &"li$ g(lap $i#a& j(las, apa&a- -i$am a$a" sa53 ma$ang* (ngan #(mi&ian &"mp"lan ana&

b(r&"li$ g(lap b"&an -imp"nan*

K"mp"lan bilangan prima g(nap

Angg3$an%a a#ala- ! #an j(las ini a#ala- -imp"nan*

K"mp"lan bin$ang bin$ang #i ang&asa

4"mla- bin$ang #i ang&asa $i#a& $(r#(?inisi #(ngan j(las &ar(na #i l"ar ba$as &(mamp"an

man"sia "n$"& m(njang&a"n%a, ma&a ini b"&an -imp"nan*

K"mp"lan 5arna in#a-P(ng(r$ian 5arna in#a- ini $i#a& j(las &ar(na b(rgan$"ng pa#a >i$arasa #an as"msi pa#a masing

masing 3rangb(rsi?a$ r(la$i?* 4a#i ini b"&an -imp"nan*

K"mp"lan p(n%a&i$ %ang #i #(ri$a 3l(- man"sia

Nama p(n%a&i$ #an j(nisn%a $i#a& j(las, apa&a- p(n%a&i$ #alam, p(n%a&i$ l"ar, #an s(bagain%a*

4a#i ini b"&an -imp"nan*

T"lis&an angg3$aangg3$a %ang $(r#apa$ #i #alam -imp"nan b(ri&"$*

P a#ala- -imp"nan nama pr(si#(n (p"bli& In#3n(sia

9 a#ala- -imp"nan bilangan g(nap %ang &"rang #ari .@*

a#ala- -imp"nan nama p"la" b(sar #i In#3n(si*

S a#ala- -imp"nan ?a&$3r #ari /< %ang &"rang #ari !@*

T a#ala- -imp"nan nama b(n"a*

U a#ala- -imp"nan nama sam"#ra*

6 a#ala- -imp"nan nama b"lan %ang b(rj"mla- /@ -ari*

a#ala- -imp"nan -(5an p(ma&an r"mp"$*

a#ala- -imp"nan &(n#araan %ang b(r3#a (mpa$*

a#ala- -imp"nan nama -ari %ang #ia5ali #(ngan -"r"? S*


8/10

P(mba-asan

P = { S"&arn3, S"gar$3, B4* Habibi(, Ab#"ra-man a-i#, M(ga5a$i S"&arn3p"$ri, S"sil3

Bambang "#-3%3n3 }*

9 = { !, 0, a>a- %ang $(r&(>il a#ala- @* Ti#a& a#a bilangan >a>a- %ang &"rang #ari @* 4a#i,

-imp"nan >a>a- %ang &"rang #ari @ m(r"pa&an -imp"nan &3s3ng*

Himp"nan nama b"lan %ang b(rj"mla- -ari /!


9/10

4"mla- -ari %ang #alam s(b"lan a#ala- !;,!;,/@, a$a" /.* Ti#a& a#a b"lan %ang m(mili&i j"mla-

-ari /!* 4a#i, -imp"nn nama b"lan %ang b(rj"mla- /! -ari m(r"pa&an -imp"nan &3s3ng*

T(n$"&a #"a -imp"nan s(m(s$a "n$"& s($iap bilangan b(ri&"$*

A = { 4a&ar$a, S(rang, Ban#"ng, S(marang, 3g%a&ar$a, S"raba%a }

B = { !, 0,


10/10

ari p(rn%a$aanp(rn%a$aan b(ri&"$, mana&a- %ang b(narQ

P(mba-asan

9P b(nar s($iap angg3$a 9 m(nja#i P*

P sala-, &ar(na a#a angg3$a %ai$" 9 %ang $i#a& m(nja#i angg3$a p

S saja, &ar(na a#a angg3$a S, %ai$" O %ang $i#a& m(nja#i angg3$a r(al

S9 b(nar, &ar(na s($iap S m(nja#i anng3$a P*

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