If `A={1,3,5,7)` and `B={2,4,6}`, find `n(AxxA)`

Answer

To find the number of elements in the Cartesian product of set A with itself, denoted as \( n(A \times A) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Sets**:
- Given \( A = \{1, 3, 5, 7\} \) and \( B = \{2, 4, 6\} \), we focus on set A for the Cartesian product \( A \times A \).

2. **Count the Elements in Set A**:
- The number of elements in set A, denoted as \( n(A) \), is 4 since \( A \) contains the elements 1, 3, 5, and 7.

3. **Use the Formula for Cartesian Product**:
- The formula for the number of elements in the Cartesian product of two sets \( A \) and \( B \) is:
\[ n(A \times B) = n(A) \times n(B) \]
- Since we are finding \( A \times A \), we can substitute \( B \) with \( A \):
\[ n(A \times A) = n(A) \times n(A) \]

4. **Calculate the Number of Elements in \( A \times A \)**:
- Substituting the value of \( n(A) \):
\[ n(A \times A) = 4 \times 4 = 16 \]

5. **Conclusion**:
- Therefore, the number of elements in the Cartesian product \( A \times A \) is 16.

### Final Answer:
\[ n(A \times A) = 16 \]