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

Answer

To solve the problem, we need to determine the elements of the relation defined by the set \( A = \{2, 3, 4, 5, 6\} \) and the condition \( x = y \).

### Step-by-Step Solution:

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

2. **Understand the Cartesian Product \( A \times A \)**:
The Cartesian product \( A \times A \) consists of all ordered pairs \( (x, y) \) where \( x \) and \( y \) are elements of set \( A \). This means we will have pairs like \( (2, 2), (2, 3), (2, 4), \ldots, (6, 6) \).

3. **Define the Relation**:
The relation is defined as \( R = \{(x, y) \in A \times A : x = y\} \). This means we are only interested in pairs where the first element is equal to the second element.

4. **List the Pairs Where \( x = y \)**:
From the set \( A \), the pairs that satisfy \( x = y \) are:
- \( (2, 2) \)
- \( (3, 3) \)
- \( (4, 4) \)
- \( (5, 5) \)
- \( (6, 6) \)

5. **Write the Final Relation**:
Therefore, the relation \( R \) can be expressed as:
\[ R = \{(2, 2), (3, 3), (4, 4), (5, 5), (6, 6)\} \]

### Final Answer:
The elements of the relation \( R \) are:
\[ R = \{(2, 2), (3, 3), (4, 4), (5, 5), (6, 6)\} \]