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Math Help - Proofs. Need help proving the following

  1. #1
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    Proofs. Need help proving the following

    Can anyone prove this?If S is a subset of D(f) then S is a subset of f^(-1)(f(S))

    So far I have:
    Let x be an element of S
    Therefore, f(x) is an element of f(s)
    f inverse of f(s) = {p is an element of D(f) | f(p) is an element of f(s)}
    since f(x) is an element of f(s), then x is an element of f inverse f(s)

    Anything else I can add or omit?
    Any help is very much appreciated!
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  2. #2
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    Re: Proofs. Need help proving the following

    Quote Originally Posted by duckyone View Post
    [COLOR=#373737][FONT=Lucida Grande]Can anyone prove this?If S is a subset of D(f) then S is a subset of f^(-1)(f(S))
    It is hard for to read your question. But I think it means:
    If f:A\to B and S\subseteq A then S\subseteq f^{-1}[f(S)]~..

    The definition gives us t\in S implies f(t)\in f(S).

    Can you finish?
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