Prove that X=Y is equivalent to P(X)=P(Y),where X,Y are sets and P(X) is Set of X's all subsets.The same goes for P(Y0

Question

Well,i haven't tried anything yet,because I've got no idea how to prove it.If possible,please help me

Also http://math.stackexchange.com/questions/332130/prove-that-mathcalpa%E2%8A%86-mathcalpb-if-and-only-if-a%E2%8A%86b and many many many others which you can find in the "Linked" section (on the right side of the screen) in both the duplicate and the question suggested in this comment. — Asaf Karagila, Apr 25 '15 at 13:20

score 1 · Answer 1 · answered Apr 25 '15 at 13:16

1

Hint. Note that $\bigcup P(X)=X$.

answered Apr 25 '15 at 13:16

Hagen von Eitzen

1 Answers1