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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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To show that if \( P(A) = P(B) \), then \( A = B \), we will follow these steps: ### Step 1: Understand the Power Set The power set \( P(A) \) of a set \( A \) is the set of all subsets of \( A \). This includes the empty set and \( A \) itself. ### Step 2: Show that \( A \subseteq B \) 1. Since \( A \) is a subset of its power set, we have \( A \in P(A) \). 2. Given that \( P(A) = P(B) \), it follows that \( A \in P(B) \). ...
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