6. Let X, Y be sets and f : X -+ Y. Prove that the following are...
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6. 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-l(f(E)) = E for all subsets E of X.
(d) f(A n B) = f(A) n f(B) for all subsets A and B of X.
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