Problem 1: Recall from the lecture notes that the (Cartesian) product of two sets A, B, written A X B, is the set {(a, b) |a e A, be B}, i.e. the set of all ordered pairs with first entry in A and second in B. Determine which of the following are true and which are false; if they are true provide a proof, if false give a counterexample. 1. 0 XN =0 2. If A x B = B X A implies A = B 3. If A = B implies that A x B = B x A 4. (AXA) X A = Ax (AXA) Problem 2: Prove that for sets A, B, C that (A - B) CC = (A-C) CB. Problem 3: Show that that for statements P, Q, R that the following compound statement is a tautology, with and without using a truth table as discussed in class: ((P = Q) V(P = R)) + (P = (Q V R)).Problem 4: For sets A, B we define the symmetric difference to be AAB = (A - B) U(B - A). Show that: 1. AAB = (AUB) - (An B) for any sets A, B. 2. If AAB = 0 then A = B