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One-to-one proof

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Let f:A->B where A and B are nonempty. Prove that f has the property f^-1(f(S))=S for every subset S of A if and only if f is one-to-one

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Solution Summary

This provides an example of completing a proof regarding a one-to-one function.

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Proof:

"=>" We consider a, b in A and f(a) = f(b). Let S = {a}, then f^-1(f(S)) = f^-1({f(a)})={a}.
But f(b) = f(a), then b is inside f^-1(f(S)) ...

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