If `mu = {1,2,3,4,5,6,7}, A = {1,2,3}`, and `B = {2,6,7}` then `(A nn B)' = ?`

Options

A. `{1,3,6,7}`
B. `{1,3,7}`
C. `{1,3,6}`
D. `{1,3,5,6,7}`

Explanation

To solve the problem, we need to find the complement of the intersection of sets A and B with respect to the universal set μ.

### Step-by-Step Solution:

1. **Identify the Universal Set (μ)**:
\[ \mu = \{1, 2, 3, 4, 5, 6, 7\} \]

2. **Identify the Sets A and B**:
\[ A = \{1, 2, 3\} \]
\[ B = \{2, 6, 7\} \]

3. **Find the Intersection of Sets A and B (A ∩ B)**:
The intersection of two sets A and B consists of the elements that are common to both sets.
\[ A \cap B = \{x : x \in A \text{ and } x \in B\} \]
Checking the elements:
- The common element is **2**.
Therefore,
\[ A \cap B = \{2\} \]

4. **Find the Complement of (A ∩ B) with respect to μ**:
The complement of a set includes all the elements in the universal set that are not in the given set.
\[ (A \cap B)' = \{x : x \in \mu \text{ and } x \notin (A \cap B)\} \]
Since \(A \cap B = \{2\}\), we need to exclude 2 from the universal set μ.
\[ (A \cap B)' = \mu - \{2\} = \{1, 3, 4, 5, 6, 7\} \]

5. **Final Result**:
\[ (A \cap B)' = \{1, 3, 4, 5, 6, 7\} \]