1. Union of sets : A U B = {x / x є A or x є B or x є A and x є B }

Note:

A U A = A

A n A = A

A n A’= {}

A U A’= U

2. Intersection of sets: A n B = {x / x є A and x є B }

Properties of set difference

1. Set difference is not commutative A – B ≠ B – A

2. Set difference is not associative A– (B – C) ≠ (A – B) – C

Distributive Property

1. Union is distributed over intersection A U (B n C) = (A U B ) n (AU C)

2. Intersection is distributed over union A n ( B U C) = (A n B) U (A n C)

DE Morgan’s Laws

1. Regarding complementation

(i) (A U B)’ = A’ n B’

(ii) (A n B)’ = A’ U B’

2. Regarding set difference

(i) A – (B U C) = (A – B) n (A – C)

(ii) A – (B n C) = (A – B) U (A – C)

♦ n(A U B) = n (A) + n (B) – n(A n B) if A n B ≠ { }

♦ n(A U B) = n (A) + n (B) if A n B = { }

- n(A U B U C) = n (A) + n (B) + n (C)–n(A n B)–n(B n C)–n(A n C) + n(A n B n C)

## No comments:

Post a Comment