1. Prove that (p q) [(p q)] (p q). In Problems 23 A, B, and C are sets. Verify each set equal- ity. 2. A \(B C) = (A \B)(A \C). 3. A \(B \C) = (A \B)(A C). 4. Let A = N, B = Z8, C = 2Z= {even integers}. Illus- trate the truth of Problems 2 and 3 by identifying the LHS and RHS of each equality when these particular sets A, B, and C are used.