Let A = {1,2,3}. For `x,yinA`, let xRy if and only if `xgty`. Write down R as subset of `AxxA`.

Answer

To solve the problem, we need to find the relation \( R \) defined on the set \( A = \{1, 2, 3\} \) where \( xRy \) if and only if \( x > y \). We will express \( R \) as a subset of \( A \times A \).

### Step-by-Step Solution:

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

2. **Determine \( A \times A \)**:
The Cartesian product \( A \times A \) consists of all possible ordered pairs \( (x, y) \) where \( x \) and \( y \) are elements of \( A \).
\[ A \times A = \{(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)\} \]

3. **Apply the Relation Condition**:
We need to find the pairs \( (x, y) \) such that \( x > y \). We will check each pair in \( A \times A \):
- \( (1, 1) \): Not included (1 is not greater than 1)
- \( (1, 2) \): Not included (1 is not greater than 2)
- \( (1, 3) \): Not included (1 is not greater than 3)
- \( (2, 1) \): Included (2 is greater than 1)
- \( (2, 2) \): Not included (2 is not greater than 2)
- \( (2, 3) \): Not included (2 is not greater than 3)
- \( (3, 1) \): Included (3 is greater than 1)
- \( (3, 2) \): Included (3 is greater than 2)
- \( (3, 3) \): Not included (3 is not greater than 3)

4. **Collect the Valid Pairs**:
From the above checks, the pairs that satisfy \( x > y \) are:
\[ R = \{(2, 1), (3, 1), (3, 2)\} \]

5. **Final Answer**:
Therefore, the relation \( R \) as a subset of \( A \times A \) is:
\[ R = \{(2, 1), (3, 1), (3, 2)\} \]