Hukum-hukum himpunan
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Himpunan
Transcript of Hukum-hukum himpunan
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5/20/2018 Hukum-hukum himpunan
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Hukum-hukum HimpunanHukum identitas
A = A
A S = A
Hukum nullatau dominasi
A =
A S = S
Hukum komplemen
A A = S
A
A
=
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Hukum-hukum HimpunanHukum idempotent
A A = A
A S = A
Hukum involusi
A = A
Hukum penyerapan (absorpsi)
A (A B) = A
A (A B) = A
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Hukum-hukum HimpunanHukum komutatif
A B = B A
A B = B A
Hukum asosiatif
A (B C) = (A B) C
A (B C) = (A B) C
Hukum distributif
A (B C) = (A B) (A C)
A (B C) = (A B) (A C)
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Hukum-hukum HimpunanHukum De Morgan
(A B)
= A B
(A B)
= A B
Hukum 0/1
= S
S =
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Pembuktian Hukum/Dalil De MorganDiketahui : Himpunan S = {1, 2, 3, 4, 5, 6}
Himpunan A = {1, 2, 3}
Himpunan B = {3, 4}
Ditanya : Buktikan kedua dalil atau hukum De Morgan . . . ?
Jawaban :A B = {3}
(A B)
= {1, 2, 4, 5, 6}
A = {4, 5, 6}
B = {1, 2, 5, 6}
A B = {4, 5, 6} {1, 2, 5, 6} = {1, 2, 4, 5, 6}
Jadi, (A B)
= A B
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Pembuktian Hukum/Dalil De MorganA B = {1, 2, 3, 4}
(A B)
= {5, 6}
A = {4, 5, 6}
B = {1, 2, 5, 6}
A B = {3}A B = {4, 5, 6} {1, 2, 5, 6} = {5, 6}
Jadi, (A B)
= A B
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Sifat-sifat yang Berlaku Pada Operasi Himpunan yaitu:
1.n(S) = n(A B) + n(A B)
2.n(A B) = n(A) + n(B) n(A B)
3.n(S) = n(A) + n(B) n(A B) + n(A B)
4.n(A) = n(S) - n(A)
5.n(A B) = n(A) + n(B) n(A B)
6.n(A + B) = n(A B) n(A B)
7.n(A - B) = n(A) n(A B)
8.n(A + A) = 0
9.n(A S) = n(S)
10.n(A S) = n(A)
11.n(A - S) = 012.n(A A) = n(S)
13.n(A A) = 0
