If `n(AxxB)=45`, then `n (A)` cannot be

Options

A. 15
B. 17
C. 5
D. 9

Answer

To solve the problem, we need to determine which value of \( n(A) \) cannot be a possibility given that \( n(A \times B) = 45 \).

### Step-by-Step Solution:

1. **Understanding Cartesian Product**:
The number of elements in the Cartesian product of two sets \( A \) and \( B \) 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 \( B \).

2. **Given Information**:
We know that:
\[ n(A \times B) = 45 \]
Therefore, we can write:
\[ n(A) \times n(B) = 45 \]

3. **Finding Factors of 45**:
To find possible values for \( n(A) \), we need to identify the factors of 45. The factors of 45 are:
- 1
- 3
- 5
- 9
- 15
- 45

4. **Evaluating Options**:
We need to check which of the given options cannot be a value for \( n(A) \). The options provided include:
- 15
- 17
- 5
- 9

From the factors of 45, we can see:
- 15 is a factor of 45 (possible)
- 5 is a factor of 45 (possible)
- 9 is a factor of 45 (possible)
- 17 is **not** a factor of 45 (not possible)

5. **Conclusion**:
Since 17 is not a factor of 45, it cannot be the number of elements in set \( A \). Therefore, the answer is:
\[ n(A) \text{ cannot be } 17 \]

### Final Answer:
\( n(A) \) cannot be 17.