If P = {2, 3}, then `P xx P` is equal to

Options

A. {(2, 3), (3, 2)}
B. {2, 2), (3, 3)}
C. {(2,2),(2,3), (3,2)}
D. {(2,2), (2,3), (3,2), (3,3)}

Answer

To find \( P \times P \) where \( P = \{2, 3\} \), we need to compute the Cartesian product of set \( P \) with itself. The Cartesian product \( P \times P \) consists of all possible ordered pairs where the first element comes from the first set \( P \) and the second element comes from the second set \( P \).

### Step-by-Step Solution:

1. **Identify the Set**:
We have the set \( P = \{2, 3\} \).

2. **Define the Cartesian Product**:
The Cartesian product \( P \times P \) is defined as:
\[ P \times P = \{(a, b) | a \in P, b \in P\} \]

3. **List All Possible Ordered Pairs**:
We will create ordered pairs by taking each element from the first set \( P \) and pairing it with each element from the second set \( P \):
- Pairing \( 2 \) with \( 2 \): \( (2, 2) \)
- Pairing \( 2 \) with \( 3 \): \( (2, 3) \)
- Pairing \( 3 \) with \( 2 \): \( (3, 2) \)
- Pairing \( 3 \) with \( 3 \): \( (3, 3) \)

4. **Combine the Ordered Pairs**:
Now we can combine all the ordered pairs we have formed:
\[ P \times P = \{(2, 2), (2, 3), (3, 2), (3, 3)\} \]

5. **Final Answer**:
Therefore, the Cartesian product \( P \times P \) is:
\[ P \times P = \{(2, 2), (2, 3), (3, 2), (3, 3)\} \]