Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, the `Auu(BnnC)` is

Options

A. {3}
B. {1, 2, 3, 4}
C. {1, 2, 5, 6}
D. {1, 2, 3, 4, 5, 6}

Explanation

To solve the problem, we need to find \( A \cup (B \cap C) \) where:

- \( A = \{1, 2, 3\} \)
- \( B = \{3, 4\} \)
- \( C = \{4, 5, 6\} \)

### Step 1: Find \( B \cap C \)

The intersection \( B \cap C \) consists of elements that are common to both sets \( B \) and \( C \).

- Set \( B = \{3, 4\} \)
- Set \( C = \{4, 5, 6\} \)

The common element in both sets is \( 4 \).

Thus,
\[ B \cap C = \{4\} \]

### Step 2: Find \( A \cup (B \cap C) \)

Now, we need to find the union of set \( A \) with the result from the previous step \( (B \cap C) \).

- Set \( A = \{1, 2, 3\} \)
- Set \( B \cap C = \{4\} \)

The union \( A \cup (B \cap C) \) combines all unique elements from both sets.

Thus,
\[ A \cup (B \cap C) = \{1, 2, 3\} \cup \{4\} \]

This results in:
\[ A \cup (B \cap C) = \{1, 2, 3, 4\} \]

### Final Answer

The final answer is:
\[ A \cup (B \cap C) = \{1, 2, 3, 4\} \]

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