If `A= {1,2,3,6} and B= (2,4,6)` be two sets of universal set U= {1,2,3,4,5,6,7}. Then, `(A' nn B')` is equal to

Options

A. {2,4,7}
B. `phi`
C. {5,7}
D. {4,6}

Answer

To solve the problem, we need to find the intersection of the complements of two sets \( A \) and \( B \) with respect to the universal set \( U \).

### Step-by-step Solution:

1. **Identify the Sets**:
- Given sets:
- \( A = \{1, 2, 3, 6\} \)
- \( B = \{2, 4, 6\} \)
- Universal set:
- \( U = \{1, 2, 3, 4, 5, 6, 7\} \)

2. **Find the Complement of Set A (\( A' \))**:
- The complement of \( A \) consists of all elements in the universal set \( U \) that are not in \( A \).
- \( A' = U - A = \{1, 2, 3, 4, 5, 6, 7\} - \{1, 2, 3, 6\} \)
- Removing the elements of \( A \) from \( U \):
- Remaining elements: \( 4, 5, 7 \)
- Therefore, \( A' = \{4, 5, 7\} \)

3. **Find the Complement of Set B (\( B' \))**:
- The complement of \( B \) consists of all elements in the universal set \( U \) that are not in \( B \).
- \( B' = U - B = \{1, 2, 3, 4, 5, 6, 7\} - \{2, 4, 6\} \)
- Removing the elements of \( B \) from \( U \):
- Remaining elements: \( 1, 3, 5, 7 \)
- Therefore, \( B' = \{1, 3, 5, 7\} \)

4. **Find the Intersection of \( A' \) and \( B' \) (\( A' \cap B' \))**:
- Now we need to find the common elements between \( A' \) and \( B' \).
- \( A' = \{4, 5, 7\} \)
- \( B' = \{1, 3, 5, 7\} \)
- The common elements are \( 5 \) and \( 7 \).
- Therefore, \( A' \cap B' = \{5, 7\} \)

### Final Answer:
Thus, \( (A' \cap B') = \{5, 7\} \).

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