4. (a) Use Venn Diagrams to prove each of the following. i. A - B = A B'

ii. (A - B) - C = A B' C'

(b) Use algebraic method to prove each of the follwoing set equalities. Hint: The rules stated in the above table, such as Associate law, DeMorgan law, and Distributiuve law, apply only to intersection and union operations. They do NOT apply to other operations such as set difference. To deal with set difference, it is helpful to first replace set difference with the corresponding rule that uses set complement. i. A - (B - C) = (A B') U (A C) ii. (A - B)' = A' U B iii. A (A B)' = A - B

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