Question

For any two sets A and B, If $P\left(A\right)=P\left(B\right),ShowthatA=B$

Answer 1

$P\left(A\right)$ is the power set of A and $P\left(B\right)$ is the power set of B. Since it is given that $P\left(A\right)=P\left(B\right)$, then, this means the power sets of A and B are equal, this implies that the subsets of two sets A and B are equal.

Therefore , A and B should contain the same elements.

$A=B$.

Hence proved.