If `AxxB={(1,2),(1,3),(1,6),(7,2),(7,3),(7,6)}` then find sets A and B.

Explanation

To find the sets A and B from the given Cartesian product \( A \times B = \{(1,2),(1,3),(1,6),(7,2),(7,3),(7,6)\} \), we can follow these steps:

### Step 1: Identify the first elements of the ordered pairs
The first elements of each ordered pair in the set \( A \times B \) represent the elements of set A.

From the pairs:
- (1, 2)
- (1, 3)
- (1, 6)
- (7, 2)
- (7, 3)
- (7, 6)

The first elements are 1 and 7.

### Step 2: Determine set A
From the first elements identified, we can conclude that:
\[ A = \{1, 7\} \]

### Step 3: Identify the second elements of the ordered pairs
The second elements of each ordered pair in the set \( A \times B \) represent the elements of set B.

From the pairs:
- (1, 2)
- (1, 3)
- (1, 6)
- (7, 2)
- (7, 3)
- (7, 6)

The second elements are 2, 3, and 6.

### Step 4: Determine set B
From the second elements identified, we can conclude that:
\[ B = \{2, 3, 6\} \]

### Final Answer
Thus, the sets A and B are:
\[ A = \{1, 7\} \]
\[ B = \{2, 3, 6\} \]

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