Let R be the relation in the set N given by R = `{a,b):a` is a multiple of b} .Then :

Options

A. `(2,3)inR`
B. `(4,6)inR`
C. `(3,9)inR`
D. `(7,24)inR`

Answer

To determine which pairs satisfy the relation R = {(a, b) : a is a multiple of b} in the set of natural numbers N, we will analyze each option step by step.

### Step-by-step Solution:

1. **Understanding the Relation**: The relation R states that for a pair (a, b), 'a' must be a multiple of 'b'. This means there exists some integer k such that a = b * k.

2. **Checking Option 1**: (2, 3)
- We need to check if 2 is a multiple of 3.
- Since 2 divided by 3 does not yield an integer (2/3 = 0.67), 2 is not a multiple of 3.
- **Conclusion**: Option 1 is incorrect.

3. **Checking Option 2**: (4, 6)
- We need to check if 4 is a multiple of 6.
- Since 4 divided by 6 does not yield an integer (4/6 = 0.67), 4 is not a multiple of 6.
- **Conclusion**: Option 2 is incorrect.

4. **Checking Option 3**: (3, 9)
- We need to check if 9 is a multiple of 3.
- Since 9 divided by 3 equals 3 (9/3 = 3), 9 is a multiple of 3.
- **Conclusion**: Option 3 is correct.

5. **Checking Option 4**: (7, 24)
- We need to check if 24 is a multiple of 7.
- Since 24 divided by 7 does not yield an integer (24/7 = 3.43), 24 is not a multiple of 7.
- **Conclusion**: Option 4 is incorrect.

### Final Conclusion:
The only pair that satisfies the relation R is option 3: (3, 9).