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If A and B are any two sets, prove that ...

If A and B are any two sets, prove that
P(A) = P(B) implies A = B.

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To prove that if \( P(A) = P(B) \) then \( A = B \), we will follow a structured approach. ### Step-by-step Solution: 1. **Understanding Power Sets**: The power set \( P(A) \) of a set \( A \) is defined as the set of all possible subsets of \( A \), including the empty set and \( A \) itself. Similarly, \( P(B) \) is the set of all subsets of \( B \). 2. **Assumption**: ...
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