1. The problem statement, all variables and given/known data Can you conclude that A = B if A and B are two sets with the same power set? 2. Relevant equations 3. 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.