Let R be the relation in set N, given by `R= {(a,b): a = b-2,b gt 6}`. Then,

Options

A. `(8,7) inR`
B. `(6,8) inR`
C. `(3,8) inR`
D. `(2,4) inR`

Answer

To solve the problem, we need to analyze the relation \( R \) defined on the set of natural numbers \( N \) by the condition:

\[ R = \{(a, b) : a = b - 2, b > 6\} \]

We will check each option to see if it belongs to the relation \( R \).

### Step-by-Step Solution:

1. **Option 1: (8, 7)**
- Check if \( a = b - 2 \):
\[ 8 = 7 - 2 \quad \text{(This is false, since } 7 - 2 = 5\text{)} \]
- Since the first condition is false, (8, 7) does not belong to \( R \).

2. **Option 2: (6, 8)**
- Check if \( a = b - 2 \):
\[ 6 = 8 - 2 \quad \text{(This is true, since } 8 - 2 = 6\text{)} \]
- Now check the second condition \( b > 6 \):
\[ 8 > 6 \quad \text{(This is true)} \]
- Since both conditions are satisfied, (6, 8) belongs to \( R \).

3. **Option 3: (3, 8)**
- Check if \( a = b - 2 \):
\[ 3 = 8 - 2 \quad \text{(This is false, since } 8 - 2 = 6\text{)} \]
- Since the first condition is false, (3, 8) does not belong to \( R \).

4. **Option 4: (2, 4)**
- Check if \( a = b - 2 \):
\[ 2 = 4 - 2 \quad \text{(This is true, since } 4 - 2 = 2\text{)} \]
- Now check the second condition \( b > 6 \):
\[ 4 > 6 \quad \text{(This is false)} \]
- Since the second condition is not satisfied, (2, 4) does not belong to \( R \).

### Conclusion:
Only the second option (6, 8) belongs to the relation \( R \).

### Final Answer:
The correct option is (6, 8).

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