Operasi Himpunan
Operasi Himpunan
Jenis Operasi | Hukum dan sifat-sifat Operasi | |
1 | Gabunan (Union) | A U B = B U A disebut sifat komutatif gabungan (A U B) U C = A U (B U C) disebut sifat asosiatif gabungan A U Ø = A A U U = U A U A = A A U A’ = U Disebut sifat pelengkap gabungan |
2 | Irisan (intersection) | A W B = B W A disebut sifat komutatif irisan A W A = A A W A W U = A A W A’ = Ø disebut sifat pelengkap irisan (A W B) W C = A W (B W A) disebut sifat asosiatif irisan |
2 | Distributif | A U (B W C) = (A U B) W (A U C); disebut sifat distributif adonan terhadap irisan. A W (B U C) = (A W B) U (A W C); disebut sifat distributif irisan terhadap gabungan. |
3 | Selisih | A – A = Ø A – Ø = A A – B = A W B’ A – (BUC) = (A – B)W (A – C) A – (B W C) = (A – B)U(A – C) |
4 | Komplemen | (A’)’ = A U’ = Ø Ø’ = U AUA’ = U AWA’ = U AWA’= Ø |
5 | Banyaknya Anggota | n(A) + n(B) K n(AUB) n(AUB) = n(A) + n(B) – n(AWB) n(AUBUC) = n(A) + n(B) + n(C) – n(AWB) – n(BWC) – n(CWA) + n(AWBWC) n(A) + n(B) = n(AUB) + n(AWB) n(A) + n(B) + n(C) =n(AUBUC) + n(AWB) + n(AWC) + n(BWC) – n(AWBWC) |
A irisan B ditulis A ∩ B = {x | x ∈ A dan x ∈ B}
Contoh : A= {1, 2, 3, 4, 5}
B= {2, 3, 5, 7, 11}
A ∩ B = {2, 3, 5}
2. Gabungan Himpunan
A adonan B ditulis A ∪ B = {x | x ∈ A atau x ∈ B}
Contoh : A= {1, 2, 3, 4, 5}
B= {2, 3, 5, 7, 11}
A ∪ B = {1, 2, 3, 4, 5, 7, 11}
3. Selisih
A Selisih B ditulis A-B = {x | x ∈ A atau x Ï B}
Contoh : A= {1, 2, 3, 4, 5}
B= {2, 3, 5, 7, 11}
A-B = {1, 4}
4. Komplemen himpunan
Komplemen A ditulis A1 atau Ac = {x | x ∈ S dan x Ï A}
Contoh : A= {1, 2, … , 5}
S = {bil. Asli kurang dari 10}
Ac = {6, 7, 8, 9} Sumber http://pusat-matematika.blogspot.com
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