Let A and B be two sets such that
`AxxB = {(a, 1), (b, 3), (a, 3), (b, 1), (a, 2), (b, 2)}`
Then,

Options

A. A = {1, 2, 3} and B = {a, b}
B. A = {a, b} and B = {1, 2, 3}
C. A = {1, 2, 3} and `B sub {a, b}`
D. `A sub {a,b} and B sub {1, 2, 3}`

Explanation

To solve the problem, we need to identify the sets A and B based on the given Cartesian product \( A \times B = \{(a, 1), (b, 3), (a, 3), (b, 1), (a, 2), (b, 2)\} \).

### Step-by-Step Solution:

1. **Understanding Cartesian Product**:
The Cartesian product \( A \times B \) consists of all possible ordered pairs where the first element is from set A and the second element is from set B.

2. **Identifying Elements in A and B**:
From the given pairs:
- The first elements of the pairs are \( a \) and \( b \).
- The second elements of the pairs are \( 1, 2, \) and \( 3 \).

Thus, we can deduce:
- Set \( A = \{a, b\} \)
- Set \( B = \{1, 2, 3\} \)

3. **Verifying the Cartesian Product**:
Now, let's verify if these sets produce the given Cartesian product:
- The pairs generated from \( A \) and \( B \) would be:
- \( (a, 1) \)
- \( (a, 2) \)
- \( (a, 3) \)
- \( (b, 1) \)
- \( (b, 2) \)
- \( (b, 3) \)

This gives us the complete set of pairs:
\[ A \times B = \{(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)\} \]

4. **Matching with Given Product**:
The given Cartesian product is:
\[ \{(a, 1), (b, 3), (a, 3), (b, 1), (a, 2), (b, 2)\} \]
We can see that all pairs from the derived Cartesian product are present in the given set, confirming our sets are correct.

5. **Final Conclusion**:
Therefore, the sets are:
- \( A = \{a, b\} \)
- \( B = \{1, 2, 3\} \)