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Math Help - Is this proof correct?

  1. #1
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    Is this proof correct?

    Let f: A -> B and X be subsets of A.

    Prove: X is a subset of f inverse of f(X)

    Let b be in f(X) which implies b=f(a) where a is in X
    f inverse of b=f inverse of f(a)=a which implies f inverse of b is in X
    which implies X is a subset of f inverse of f(X)

    qed

    Did I do this correctly?

    Thanks!
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  2. #2
    Senior Member TheAbstractionist's Avatar
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    Quote Originally Posted by economanc View Post
    Let f: A -> B and X be subsets of A.

    Prove: X is a subset of f inverse of f(X)

    Let b be in f(X) which implies b=f(a) where a is in X
    f inverse of b=f inverse of f(a)=a which implies f inverse of b is in X
    which implies X is a subset of f inverse of f(X)

    qed

    Did I do this correctly?

    Thanks!
    Hi economanc.

    The correct way is to start by letting a be in X and then proceed to show that a is in f^{-1}\left(f(X)\right).
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