In each of the following, state which of the ordered pairs belong to the given relations? `{(x,y):xgty+5},(1,0),(8,2),(0,1),(2,8),(9,3),(10,7),(123,4)`

Answer

To determine which of the ordered pairs belong to the relation defined by the condition \( x > y + 5 \), we will evaluate each ordered pair one by one.

### Step-by-Step Solution:

1. **Evaluate the pair (1, 0)**:
- Here, \( x = 1 \) and \( y = 0 \).
- Check the condition: \( 1 > 0 + 5 \) → \( 1 > 5 \) (False)
- Conclusion: (1, 0) does not belong to the relation.

2. **Evaluate the pair (8, 2)**:
- Here, \( x = 8 \) and \( y = 2 \).
- Check the condition: \( 8 > 2 + 5 \) → \( 8 > 7 \) (True)
- Conclusion: (8, 2) belongs to the relation.

3. **Evaluate the pair (0, 1)**:
- Here, \( x = 0 \) and \( y = 1 \).
- Check the condition: \( 0 > 1 + 5 \) → \( 0 > 6 \) (False)
- Conclusion: (0, 1) does not belong to the relation.

4. **Evaluate the pair (2, 8)**:
- Here, \( x = 2 \) and \( y = 8 \).
- Check the condition: \( 2 > 8 + 5 \) → \( 2 > 13 \) (False)
- Conclusion: (2, 8) does not belong to the relation.

5. **Evaluate the pair (9, 3)**:
- Here, \( x = 9 \) and \( y = 3 \).
- Check the condition: \( 9 > 3 + 5 \) → \( 9 > 8 \) (True)
- Conclusion: (9, 3) belongs to the relation.

6. **Evaluate the pair (10, 7)**:
- Here, \( x = 10 \) and \( y = 7 \).
- Check the condition: \( 10 > 7 + 5 \) → \( 10 > 12 \) (False)
- Conclusion: (10, 7) does not belong to the relation.

7. **Evaluate the pair (123, 4)**:
- Here, \( x = 123 \) and \( y = 4 \).
- Check the condition: \( 123 > 4 + 5 \) → \( 123 > 9 \) (True)
- Conclusion: (123, 4) belongs to the relation.

### Summary of Results:
- The ordered pairs that belong to the relation \( x > y + 5 \) are:
- (8, 2)
- (9, 3)
- (123, 4)