(a) Disprove by counterexample that for all sets A, B,C in some universe U,AUBU-UBu (b) Prove that (A- C)n(C- B)-. Hint: use proof by contradiction. (c) Prove that for any sets A and B, powerset P(AnB)PA)nP(B). Hint: show that every element of P(An B) is an element of P(A) nP(B), and vice verss (d) Let g: A- B and f: BCbe one-to-one functions, where A, B, C are arbitrary sets. Prove that their composition g: A-+