1. Use Venn diagrams with three overlapping circles to illustrate each identity. (a) A ∪ (B ∩ C ) = (A ∪ B) ∩ (A ∪ C ) (b) A\(B ∪ C) = (A \B) ∩ (A \C ) 2. Let A and B be subsets of a universal set U....

1. Use Venn diagrams with three overlapping circles to illustrate each identity.

(a) A ∪ (B ∩ C ) = (A ∪ B) ∩ (A ∪ C )

(b) A\(B ∪ C) = (A \B) ∩ (A \C )

2. Let A and B be subsets of a universal set U. Simplify each of the following expressions.

(a) (A ∪ B) ∪ (U \A)

(b) (A ∩ B) ∩ (U \A)

(c) A ∩ [B ∪ (U \A)]

(d) A ∪ [B ∩ (U \A)]

(e) (A ∪ B) ∩ [A ∪ (U \B)]

(f ) (A ∩ B) ∪ [A ∩ (U \B)]