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Math Help - Proving an equation

  1. #1
    Junior Member
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    Proving an equation



    My textbook says this is obvious, but I don't see how it is

    How is this true?

    Thanks
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by 6DOM View Post


    My textbook says this is obvious, but I don't see how it is

    How is this true?

    Thanks
    Proof of f^{-1}(A^c)\subseteq(f^{-1}(A))^c:

    x\in f^{-1}(A^c)\implies f(x)\in A^c\implies f(x)\notin A\implies x\notin f^{-1}(A)\implies x\in(f^{-1}(A))^c

    For the other direction, just flip the implication arrows. (This reasoning works in both directions.)
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