Exercises notations and conventions Unless otherwise stated, we follow the as given in Scheinerman's text. In addition, you cannot use Venn diagram(s) as proofs. 1. (15 point) Let A, B and C be sets. Present a direct proof for the following: If C A and C B, then C A n B. 2. (15 point) Let A, B and C be sets. Present a direct proof for the following: A-(BUC) = (A-B) n (A-C). 3. Let A, B and C be sets (a) (15 point) Present a direct proof for the following: (A-B)-CS A (B -C). Give a counterexample and provide a precise (b) (10 point) explanation to the following false statement: 4. Let A and B be sets. (a) (15 point) Present a direct proof for the following (b) (10 point) Give a counterexample and provide a precise explanation to the following false statement 5. (20 point) Present a direct proof for the following: Let A, B, C and D be sets. Then (An B) (C n D) = (A C) n (B D)