If `A xx B = {(a, x), (a, y), (b, x), b, y)}`, then A is equal to

Options

A. {a, x}
B. {b, y}
C. {a, b}
D. {b, x}

Answer

To solve the problem, we need to analyze the given set \( A \times B = \{(a, x), (a, y), (b, x), (b, y)\} \) and determine the set \( A \).

### Step-by-Step Solution:

1. **Understanding the Cartesian Product**:
The Cartesian product \( A \times B \) consists of all possible ordered pairs where the first element comes from set \( A \) and the second element comes from set \( B \).

2. **Identifying Elements**:
From the given set \( A \times B = \{(a, x), (a, y), (b, x), (b, y)\} \), we can see that:
- The first elements of the pairs are \( a \) and \( b \).
- The second elements of the pairs are \( x \) and \( y \).

3. **Determining Set A**:
Since the first elements of the pairs in \( A \times B \) are \( a \) and \( b \), we can conclude that:
\[ A = \{a, b\} \]

4. **Conclusion**:
Therefore, the set \( A \) is equal to \( \{a, b\} \).

### Final Answer:
\[ A = \{a, b\} \]