If the set A has p elements, B has q elements, then the number of elements in A`xx`B is

Options

A. p+q+1
B. pq
C. `p^2`
D. p+q

Answer

To find the number of elements in the Cartesian product of two sets \( A \) and \( B \), denoted as \( A \times B \), we follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Cartesian Product**:
The Cartesian product \( A \times B \) is defined as the set of all ordered pairs \( (a, b) \) where \( a \) is an element of set \( A \) and \( b \) is an element of set \( B \).

2. **Identify the Number of Elements in Each Set**:
- Let the number of elements in set \( A \) be \( p \).
- Let the number of elements in set \( B \) be \( q \).

3. **Calculate the Number of Ordered Pairs**:
Each element of set \( A \) can be paired with each element of set \( B \). Therefore, the total number of ordered pairs (elements in \( A \times B \)) is given by multiplying the number of elements in set \( A \) by the number of elements in set \( B \).

\[ \text{Number of elements in } A \times B = p \times q \]

4. **Conclusion**:
Thus, the number of elements in the Cartesian product \( A \times B \) is \( p \times q \).

### Final Answer:
The number of elements in \( A \times B \) is \( p \times q \).

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