(adsbygoogle = window.adsbygoogle || []).push({}); 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Showing a bijection between a set of functions and a set of relations

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**