If A = {2, 3, 7, 9} and `n(A xx B) = 12`, then the number of elements in set B is

Options

A. 4
B. 3
C. 2
D. 8

Answer

To solve the problem, we need to find the number of elements in set B given that the Cartesian product \( A \times B \) has 12 elements and set A has 4 elements.

### Step-by-Step Solution:

1. **Identify the number of elements in set A**:
Set \( A = \{2, 3, 7, 9\} \) has 4 elements. Therefore,
\[ n(A) = 4 \]

2. **Use the formula for the number of elements in the Cartesian product**:
The number of elements in the Cartesian product \( A \times B \) is given by the formula:
\[ n(A \times B) = n(A) \times n(B) \]
We know that \( n(A \times B) = 12 \).

3. **Substitute the known values into the formula**:
Substitute \( n(A) \) and \( n(A \times B) \) into the formula:
\[ 12 = 4 \times n(B) \]

4. **Solve for \( n(B) \)**:
To find \( n(B) \), divide both sides of the equation by 4:
\[ n(B) = \frac{12}{4} = 3 \]

5. **Conclusion**:
Therefore, the number of elements in set B is:
\[ n(B) = 3 \]

### Final Answer:
The number of elements in set B is **3**.