If A=B then show that P(A)=P(B)

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Solution

of set A are the elements of A.
Two sets are equal when they have the same elements.
P(A) = P(B)
The power sets of A and B are equal, this implies subsets of two sets A and B are equal
Therefore A and B should contain the same elements.
Hence If P(A) = P(B) then A = B.

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