If A = {2, 3, 5}, B = {2, 5, 6}, then `(A - B) xx (AnnB)` is

Options

A. `{(3,2),(3,3),(3,5)}`
B. `{(3,2),(3,5),(3,6)}`
C. `{(3,2),(3,5)}`
D. None of these

Answer

To solve the problem, we need to find the Cartesian product of the difference of sets A and B, denoted as \( A - B \), and the intersection of sets A and B, denoted as \( A \cap B \).

### Step-by-Step Solution:

1. **Identify the Sets**:
- Given \( A = \{2, 3, 5\} \)
- Given \( B = \{2, 5, 6\} \)

2. **Find \( A - B \)**:
- The difference \( A - B \) consists of elements that are in A but not in B.
- From set A, we remove the elements that are also in set B.
- Elements in A: \( 2, 3, 5 \)
- Elements in B: \( 2, 5 \)
- Removing \( 2 \) and \( 5 \) from A leaves us with \( 3 \).
- Therefore, \( A - B = \{3\} \).

3. **Find \( A \cap B \)**:
- The intersection \( A \cap B \) consists of elements that are common to both sets A and B.
- Common elements in A and B are \( 2 \) and \( 5 \).
- Therefore, \( A \cap B = \{2, 5\} \).

4. **Calculate the Cartesian Product \( (A - B) \times (A \cap B) \)**:
- Now we need to find the Cartesian product of \( A - B \) and \( A \cap B \).
- We have \( A - B = \{3\} \) and \( A \cap B = \{2, 5\} \).
- The Cartesian product \( (A - B) \times (A \cap B) \) is formed by pairing each element of \( A - B \) with each element of \( A \cap B \).
- Thus, we have:
- Pairing \( 3 \) with \( 2 \) gives \( (3, 2) \)
- Pairing \( 3 \) with \( 5 \) gives \( (3, 5) \)
- Therefore, \( (A - B) \times (A \cap B) = \{(3, 2), (3, 5)\} \).

### Final Answer:
The result of \( (A - B) \times (A \cap B) \) is \( \{(3, 2), (3, 5)\} \).