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Math Help - Pre-Image / Image proof

  1. #1
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    Pre-Image / Image proof

    I'm new to topology and have a pretty basic proof to perform but haven't had much experience with proofs and could use some help,

    Question asks, to prove that if f: A -> B and X is a subset of A

    prove that X is a subset of f^-1( f(X)) i.e that X is a subset of the pre-image of the image of X,

    this makes perfect sense to me that it's true but i'm unsuer how to construct the proof any help would be appreciated, cheers.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Re: Pre-Image / Image proof

    Quote Originally Posted by monster View Post
    Question asks, to prove that if f: A -> B and X is a subset of A prove that X is a subset of f^-1( f(X)) i.e that X is a subset of the pre-image of the image of X,
    If x\in X then, f(x)\in f(X) . But by definition, f^{-1}(f(X))=\{y\in A:f(y)\in f(X)\} , then, x satisfies the condition for being in f^{-1}(f(X)) . As a consequence, X\subset f^{-1}(f(X)) .
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