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Showing a bijection between a set of functions and a set of relations

  1. Apr 21, 2012 #1
    1. The problem statement, all variables and given/known data
    With X and Y being sets, I need to show that there is a bijection between the set of functions (X->P(Y)) and the set of relations P(X x Y) where P(..) is the power set symbol.

    2. Relevant equations
    P(Y) = {Z | Z subset of Y}

    3. The attempt at a solution
    I know a bijection is injective and surjective. The set of functions is {f ε P(X x P(Y)) | f is a function}. I also know that a function is bijective if it has an inverse. I am not too sure where to start or whether I am missing something. I have been trying to find a function and then show it has an inverse but I am stuck.

    Thanks for the help.
     
  2. jcsd
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