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

Explanation

To determine whether the statement \( P(A) \cup P(B) = P(A \cup B) \) is true for any sets \( A \) and \( B \), we will analyze both sides of the equation step by step.

### Step 1: Understand the Power Set
The power set \( P(X) \) of a set \( X \) is the set of all possible subsets of \( X \). For example, if \( A = \{1, 2\} \), then:
- The subsets of \( A \) are: \( \emptyset, \{1\}, \{2\}, \{1, 2\} \).
- Thus, \( P(A) = \{\emptyset, \{1\}, \{2\}, \{1, 2\}\} \).

### Step 2: Calculate \( P(A) \) and \( P(B) \)
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