1) Let A, B and C be sets. Determine whether or not the following are valid. Justify your answer by using either set identities or membership tables. You can also use a counterexample to show that two sets are not equivalent. Notice, that the difference between two sets A and B can be denoted A \ B or A B.

a) A (B C) = (A C) B (b) (A B) (B A) = (A B) (c) (A B) (B A) = (A B)

d) (A C) (B C) = A B C (e) (B C) (A C) = A C = A (A C) (f) A (B C) = A (B C)

2) Use set identities to show that the following expression is equivalent to the Universal set: ((A B) C (A B)) B

3) Use set identities to show that the following expression is equivalent to the empty set: ((A B) (A B)) ((B B) A)

4) The symmetric difference of set A and B, denoted by AB, is the set containing elements in either A or B, but not in both A and B. Answer the followings: (a) Let A = {a, e, f, y, q, w} and B = {e, x, z, q, p, f }. Find AB. (b) Draw Venn Diagram of (A B) (A B) and (A B) (B A). Conclude that AB = (A B) (A B) and AB = (A B) (B A). (c) Using set identities and part (b) show that AB = (A B) (A B)