5. For any set X, let P(X) denote the power set of X. Prove or disprove the following statements (In other words, determine whether each of the following statements is true or false, and prove your claim. If the statement is true, give a proof. If the statement is false, prove that the negation is true, i.e. give a counterexample). (a) For any sets A and B, P(AN B) = P(A) N P(B). (b) For any sets A and B, P(AUB) = P(A) U P(B). (c) For any sets A, B, and C, A\ (BUC)= (A\B)U (A\ C). %3D

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