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Math Help - Prove that if A ~ B then P(A) ~ P(B).

  1. #1
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    Prove that if A ~ B then P(A) ~ P(B).

    I have another question
    Q: Prove that if A ~ B then P(A) ~ P(B).

    first I started with stating that since A and B are equinumerous
    so there exists f:A ->B
    and suppose given a subset X of A
    then find b in B and a exists in A such f(a) = b
    and then stuck....
    Last edited by mr fantastic; November 29th 2010 at 10:38 AM. Reason: Re-titled.
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  2. #2
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    A bijection f : A -> B can be "lifted" to a bijection between P(A) and P(B). Namely, consider g(X)=\{f(x)\mid x\in X\} where X\subseteq A, i.e., g applies f to every element of X and collects the results. Prove that g : P(A) -> P(B) and that g is a bijection.
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