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## Homework Statement

Can you conclude that A = B if A and B are two sets with the same power set?

## Homework Equations

## The Attempt at a Solution

I know intuitively that A and B have to be equal, because all the individual entities in the power set (you know what I mean) have to be in both A and B. But, what I'm really after is a rigorous mathematical derivation of the theorem. I have no idea where to start. Any help would be greatly appreciated.