If `AxxB={(a,2),(b,4),(a,6),(b,2),(b,6),(a,4)}`, then find A and B.

Answer

To find the sets A and B from the given set \( A \times B = \{(a,2), (b,4), (a,6), (b,2), (b,6), (a,4)\} \), we will analyze the ordered pairs.

### Step-by-Step Solution:

1. **Identify the First Elements**:
Look at the first element of each ordered pair in the set. The first elements are:
- From (a,2): first element is 'a'
- From (b,4): first element is 'b'
- From (a,6): first element is 'a'
- From (b,2): first element is 'b'
- From (b,6): first element is 'b'
- From (a,4): first element is 'a'

Collecting these, we have: {a, b}.

2. **Identify the Second Elements**:
Now, look at the second element of each ordered pair in the set. The second elements are:
- From (a,2): second element is '2'
- From (b,4): second element is '4'
- From (a,6): second element is '6'
- From (b,2): second element is '2'
- From (b,6): second element is '6'
- From (a,4): second element is '4'

Collecting these, we have: {2, 4, 6}.

3. **Define Sets A and B**:
Based on the collected first and second elements:
- Set A = {a, b}
- Set B = {2, 4, 6}

### Final Answer:
- Set A = {a, b}
- Set B = {2, 4, 6}