Question

If A=B then show that P(A)=P(B)

Answer 1

of set A are the elements of A.
Two sets are equal when they have the same elements.
P(A) = P(B)
The power sets of A and B are equal, this implies subsets of two sets A and B are equal
Therefore A and B should contain the same elements.
Hence If P(A) = P(B) then A = B.