離散數學中基本定律

基本定律

1.  交換律： 　 A ∪ B = B∪A， A ∩ B = B ∩ A
2.  結合律：　 (A ∪ B) ∪ C = A ∪ (B∪C) = A ∪ B∪C
                          (A ∩ B) ∩ C = A ∩ (B ∩ C) = A ∩ B ∩ C
3.  分配律：     (A ∩ B) ∪C = (A∪C) ∩ (B∪C)
                          (A∪B) ∩ C = (A ∩ C) ∪(B ∩ C)
4.  德摩根律:    (A ∩ B)' = A' ∪ B'     (A ∪ B)' = A' ∩ B'　（絕對形式）
　　 　　　　　A - (B ∩ C) = (A - B) ∪ (A - C)     A - (B ∪ C) = (A - B) ∩ (A - C) (相對形式)
6.  吸收律： 　(A ∩ B) ∪ A = A    (A ∪ B) ∩ A = A
7.  零律：　　  A ∪ E = E  , 　A ∩ E = A
8.  同一律：　  A ∪ Ø = A，A ∩ E= A  ,  A ∪ E = E , A ∩ Ø = Ø
9.  矛盾律：　  A ∩ A' = Ø
10.排中律：　 A ∪ A' = E
11.餘補律：　 Ø' = E　, 　E' = Ø
12.雙重否定律： (A')' = A
13.補交轉換律： A - B = A ∩ B'