If A = {1, 2, 5, 6} and B = {1, 2, 3}, then what is `(A xx B) nn (B xx A)` equal to?

Options

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

Answer

To solve the problem, we need to find the intersection of the Cartesian products of two sets A and B, specifically \( (A \times B) \cap (B \times A) \).

### Step-by-Step Solution:

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

2. **Calculate \( A \times B \)**:
- The Cartesian product \( A \times B \) consists of all ordered pairs where the first element is from set A and the second element is from set B.
- \( A \times B = \{(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (5, 1), (5, 2), (5, 3), (6, 1), (6, 2), (6, 3)\} \)

3. **Calculate \( B \times A \)**:
- The Cartesian product \( B \times A \) consists of all ordered pairs where the first element is from set B and the second element is from set A.
- \( B \times A = \{(1, 1), (1, 2), (1, 5), (1, 6), (2, 1), (2, 2), (2, 5), (2, 6), (3, 1), (3, 2), (3, 5), (3, 6)\} \)

4. **Find the Intersection \( (A \times B) \cap (B \times A) \)**:
- Now we need to find the common elements in both sets.
- The common pairs are:
- \( (1, 1) \)
- \( (1, 2) \)
- \( (2, 1) \)
- \( (2, 2) \)

5. **Final Result**:
- Therefore, \( (A \times B) \cap (B \times A) = \{(1, 1), (1, 2), (2, 1), (2, 2)\} \)