Let A = {2, 5, 7,9} and B = {a, b, c}, then `n(A xx B)` is equal to

Options

A. 4
B. 3
C. 7
D. 12

Answer

To solve the problem, we need to find the number of elements in the Cartesian product of sets A and B, denoted as \( A \times B \).

### Step-by-Step Solution:

1. **Identify the Sets**:
- Set \( A = \{2, 5, 7, 9\} \) has 4 elements.
- Set \( B = \{a, b, c\} \) has 3 elements.

2. **Use the Formula for Cartesian Product**:
- The number of elements in the Cartesian product \( A \times B \) is given by the formula:
\[ n(A \times B) = n(A) \times n(B) \]
- Here, \( n(A) \) is the number of elements in set \( A \) and \( n(B) \) is the number of elements in set \( B \).

3. **Calculate the Number of Elements**:
- From the sets, we have:
\[ n(A) = 4 \quad \text{(since A has 4 elements)} \]
\[ n(B) = 3 \quad \text{(since B has 3 elements)} \]
- Now, substituting these values into the formula:
\[ n(A \times B) = 4 \times 3 = 12 \]

4. **Conclusion**:
- Therefore, the number of elements in the Cartesian product \( A \times B \) is \( 12 \).

### Final Answer:
\[ n(A \times B) = 12 \]