For any two sets A and B prove the following: `Ann(A^(prime)uuB)=AnnB`

Explanation

To prove that \( \text{Ann}(A' \cup B) = \text{Ann}(B) \), we will follow the steps of showing that each side is a subset of the other.

### Step 1: Show that \( \text{Ann}(A' \cup B) \subseteq \text{Ann}(B) \)

Let \( x \in \text{Ann}(A' \cup B) \). By definition of the annihilator, this means:
\[ x \cdot y = 0 \quad \text{for all } y \in A' \cup B \]
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