Question: Let X, Y be sets and f : X Y. Prove that the following are equivalent. a) f is 1-1 on X. b) f(AB)

Let X, Y be sets and f : X → Y. Prove that the following are equivalent.
a) f is 1-1 on X.
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 £ of X.
d) F(A ∩ B) = f(A) ∩ f(B) for all subsets A and B of X.

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