Explore BrainMass

Explore BrainMass

    One-to-one proof

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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

    © BrainMass Inc. brainmass.com October 9, 2019, 10:22 pm ad1c9bdddf

    Solution Preview


    "=>" 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)) ...

    Solution Summary

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