without loss of generality , there exists `x in A ` such that ` x notin B.` Then`{ x} in P(A) " whereas " ,{x} in P(B)`. Thus , `P(A) ne P(B) ` which contradicts the given condition . So , A= B Conversely , if P(A) = P(B) then all their singletone are the same Thus , A= B
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