Question

for 2 sets A and B prove
P(A)=P(B) implies A=B

Answer 1

I assume P(A) is the powerset of A

Answer 2

yes it is
@Zarkon

Answer 3

you know \[A\in P(A)\]correct?

Answer 4

yes

Answer 5

and since P(A)=P(B) then \[A\in P(B)\] right?

Answer 6

yeess...

Answer 7

P(B) is all the subsets of B therefore \[A\subseteq B\]

Answer 8

yeah

Answer 9

similarly

\[B\subseteq A\]

thus \[A=B\]

Answer 10

i get it thanks:)

Answer 11

np