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Is it true that for any sets A and B, P...

Is it true that for any sets A and B, `P (A) uuP (B) = P (Auu B)`? Justify your answer.

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To determine whether the statement \( P(A) \cup P(B) = P(A \cup B) \) holds true for any sets \( A \) and \( B \), we will analyze both sides of the equation and provide a justification. ### Step 1: Understand the Power Set The power set \( P(X) \) of a set \( X \) is the set of all possible subsets of \( X \), including the empty set and \( X \) itself. ### Step 2: Define the Sets Let’s define two sets: - Let \( A = \{1, 2\} \) ...
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