5. Prove each of the following set equalities both by Venn Diagram and by algebraic method.

(a) A - (B C) = (A - B) (A - C)

(b) A - (B C) = (A - B) (A - C)

(c) A (B - C) = (A B) - C = (A B) - (A C)

Hint: To prove the last form, use the equality A C' = A (A' C').

(d) A (B - C) = (A B) (A C') = (A B) - (A' C)

Basic Rules (Equalities) in Set Algebra Associative Laws: Commutative Laws: Distributive Laws: De Morgan's Laws: Complement Laws: X n (Y U Z) = (X Y) U (X n Z) Repetition: 0/1 Laws: Identity: Bound Laws