Let X, Y be sets with a function f : X→Y. Prove that the following are equivalent: (a) f is 1 – 1. (b) f(A – B) = f(A) – f(B) for all subsets A and B of X. (c) f-1(f(E)) = E for all subsets E of X. (d) f(An B) = f(A) n f(B) for all subsets A and B of X. A1 A2. An, the set A1 × A2 × ...

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