If ` A xx B ={ (p,q) ,(p,r) ,(m,q) , (m,r) } ` find A and B .

Answer

To solve the problem of finding sets A and B from the Cartesian product \( A \times B = \{ (p,q), (p,r), (m,q), (m,r) \} \), we can follow these steps:

### Step 1: Identify the elements of A and B
The Cartesian product \( A \times B \) consists of ordered pairs where the first element comes from set A and the second element comes from set B.

### Step 2: Extract unique first elements for set A
From the given pairs:
- The first elements are \( p, p, m, m \).
- The unique first elements are \( p \) and \( m \).

Thus, we can conclude:
\[ A = \{ p, m \} \]

### Step 3: Extract unique second elements for set B
Now, we look at the second elements from the pairs:
- The second elements are \( q, r, q, r \).
- The unique second elements are \( q \) and \( r \).

Thus, we can conclude:
\[ B = \{ q, r \} \]

### Final Result
Therefore, the sets are:
\[ A = \{ p, m \} \]
\[ B = \{ q, r \} \]