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Assume that P (A) = P (B). Show that A =...

Assume that `P (A) = P (B)`. Show that `A = B`

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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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