Given `A={2,3,4,5,6}`. List the elements of each of the following relations:
`{(x,y)inAxxA:x" is a divisor of y and "xney}`

Answer

To solve the problem, we need to find the pairs \((x, y)\) from the set \(A = \{2, 3, 4, 5, 6\}\) such that \(x\) is a divisor of \(y\) and \(x \neq y\).

### Step-by-Step Solution:

1. **Identify the Set**:
We have the set \(A = \{2, 3, 4, 5, 6\}\).

2. **Understand the Relation**:
We need to find pairs \((x, y)\) such that:
- \(x\) is a divisor of \(y\)
- \(x \neq y\)

3. **List Possible Pairs**:
We will check each element \(x\) in \(A\) to see which elements \(y\) it can divide.

- For \(x = 2\):
- \(y = 2\) (not included since \(x = y\))
- \(y = 3\) (not a divisor)
- \(y = 4\) (included, \(2 \mid 4\))
- \(y = 5\) (not a divisor)
- \(y = 6\) (included, \(2 \mid 6\))
- Pairs: \((2, 4)\), \((2, 6)\)

- For \(x = 3\):
- \(y = 2\) (not a divisor)
- \(y = 3\) (not included since \(x = y\))
- \(y = 4\) (not a divisor)
- \(y = 5\) (not a divisor)
- \(y = 6\) (included, \(3 \mid 6\))
- Pair: \((3, 6)\)

- For \(x = 4\):
- \(y = 2\) (included, \(4 \mid 2\) is false)
- \(y = 3\) (not a divisor)
- \(y = 4\) (not included since \(x = y\))
- \(y = 5\) (not a divisor)
- \(y = 6\) (not a divisor)
- No new pairs.

- For \(x = 5\):
- \(y = 2\) (not a divisor)
- \(y = 3\) (not a divisor)
- \(y = 4\) (not a divisor)
- \(y = 5\) (not included since \(x = y\))
- \(y = 6\) (not a divisor)
- No new pairs.

- For \(x = 6\):
- \(y = 2\) (not a divisor)
- \(y = 3\) (not a divisor)
- \(y = 4\) (not a divisor)
- \(y = 5\) (not a divisor)
- \(y = 6\) (not included since \(x = y\))
- No new pairs.

4. **Compile the Results**:
The pairs we found are:
- \((2, 4)\)
- \((2, 6)\)
- \((3, 6)\)

Thus, the relation \(R\) can be expressed as:
\[ R = \{(2, 4), (2, 6), (3, 6)\} \]

### Final Answer:
The elements of the relation are:
\[ R = \{(2, 4), (2, 6), (3, 6)\} \]