3. Prove each of the following set equalities by algebraic method. In the proofs, you may use the basic rules listed in the table below. Hint: If you start by distributive law, you will not find it useful. Instead, first replace the leftmost A by A U and then apply distributive law. Alternatively, you may find the below "combination rule" useful.

(a) Combination Rule: (A B) U (A B^c) = A

(b) Absorption Rule: A U (A B) = A

(c) A U (A^c B) = A U B

A (A^c U B) = A B

(d) (A B^c) U (A B) U (A^c B) = A U B

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