Question

if P(A)=P(B) for sets A and B prove that A=B

Answer 1

let the two sets A and B as A={a,b,c,d...} and B={1,2,3,4....}
P(A)=P(B) as you have given in the question
So all the element of Set A will be equal to the elements of set B so 
A=B 

Answer 2

let assume the two sets A and B as
A={1,2,3,4...}
and
 B={a,b,c,d....}
P(A)=P(B) as you have given in the question
So all the element of Set A will be equal to the elements of set B so 
hENCE 
A=B