Here's the problem: Let X and Y be sets. Let f: X --> Y, and let A be a subset of Y. Prove that f(f^{-1}(A)) is a subset of A. Any help is much appreciated!
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Originally Posted by widenerl194 Let X and Y be sets. Let f: X --> Y, and let A be a subset of Y. Prove that f(f^{-1}(A)) is a subset of A. Can you describe what $\displaystyle f(f^{-1}(A))$ looks like in set-theoretic terms? If not, there is a place for you to begin,
I think it might be f(f^-1(A)) = f(x) is an element of X such that f(x) is an element of f(A).
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