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

Answer

To find the number of elements in the Cartesian product \( A \times B \), we can follow these steps:

### Step 1: Identify the sets
We have two sets:
- \( A = \{1, 3, 5, 7\} \)
- \( B = \{2, 4, 6\} \)

### Step 2: Determine the number of elements in each set
Count the elements in set \( A \):
- \( n(A) = 4 \) (since there are 4 elements: 1, 3, 5, 7)

Count the elements in set \( B \):
- \( n(B) = 3 \) (since there are 3 elements: 2, 4, 6)

### Step 3: Use the formula for the Cartesian product
The number of elements in the Cartesian product \( A \times B \) is given by the formula:
\[ n(A \times B) = n(A) \times n(B) \]

### Step 4: Calculate the number of elements in \( A \times B \)
Substituting the values we found:
\[ n(A \times B) = n(A) \times n(B) = 4 \times 3 = 12 \]

### Conclusion
Thus, the number of elements in the Cartesian product \( A \times B \) is \( 12 \).