9. Which of the following are true for all sets A, B, and C. If the statement is true, prove it by showing each is a subset of the other. If not, provide a counterexample. (a) AU A = A. (b) BnB = B. (c) (An B)' = A' B' (d) (A')' = A (e) A\B= (B\A)' (f) (A\B) n(B\A) = 0 (g) If An B=0), then ACB. (h) BxA= A x B. (i) 0× A=0 (i) (A\B) U (B\C) =A\C. (k) (A\B) n(A\C) =A\(BUC)

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