A and B are teo sets having 3 and 5 elements respectively and having 2 elements in common. Then the number of elements in `AxxB` is

Options

A. 6
B. 36
C. 15
D. None of these

Answer

To solve the problem, we need to find the number of elements in the Cartesian product of two sets A and B, denoted as \( A \times B \).

### Step-by-step Solution:

1. **Identify the number of elements in each set:**
- Set A has 3 elements.
- Set B has 5 elements.

2. **Understand the Cartesian product:**
- The Cartesian product \( A \times B \) consists of all possible ordered pairs \( (a, b) \) where \( a \) is an element from set A and \( b \) is an element from set B.

3. **Calculate the number of elements in the Cartesian product:**
- The formula for the number of elements in the Cartesian product \( A \times B \) is given by:
\[ |A \times B| = |A| \times |B| \]
- Here, \( |A| = 3 \) and \( |B| = 5 \).

4. **Substitute the values into the formula:**
\[ |A \times B| = 3 \times 5 \]

5. **Perform the multiplication:**
\[ |A \times B| = 15 \]

6. **Conclusion:**
- The number of elements in \( A \times B \) is 15.

### Final Answer:
The number of elements in \( A \times B \) is **15**.

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