Let R be the relation in the set N given by `R = {(a , b) : a = b-2, b gt 6}`. Choose the correct answer.
(A) `(2, 4) in R`
(B) `(3, 8) in R`
(C) `(6, 8) in R`
(D) `(8, 7) in R`

Options

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

Explanation

To solve the problem, we need to analyze the relation \( R \) defined as:

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

We need to check each of the given options to see if they satisfy the conditions of the relation \( R \).

### Step 1: Analyze the options

1. **Option A: \( (2, 4) \)**
- Here, \( a = 2 \) and \( b = 4 \).
- Check if \( a = b - 2 \):
\[ 2 = 4 - 2 \quad \text{(True)} \]
- Check if \( b > 6 \):
\[ 4 > 6 \quad \text{(False)} \]
- Therefore, \( (2, 4) \notin R \).

2. **Option B: \( (3, 8) \)**
- Here, \( a = 3 \) and \( b = 8 \).
- Check if \( a = b - 2 \):
\[ 3 = 8 - 2 \quad \text{(True)} \]
- Check if \( b > 6 \):
\[ 8 > 6 \quad \text{(True)} \]
- Therefore, \( (3, 8) \in R \).

3. **Option C: \( (6, 8) \)**
- Here, \( a = 6 \) and \( b = 8 \).
- Check if \( a = b - 2 \):
\[ 6 = 8 - 2 \quad \text{(True)} \]
- Check if \( b > 6 \):
\[ 8 > 6 \quad \text{(True)} \]
- Therefore, \( (6, 8) \in R \).

4. **Option D: \( (8, 7) \)**
- Here, \( a = 8 \) and \( b = 7 \).
- Check if \( a = b - 2 \):
\[ 8 = 7 - 2 \quad \text{(False)} \]
- Therefore, \( (8, 7) \notin R \).

### Step 2: Conclusion

From the analysis, we find that:
- Option A: Not in \( R \)
- Option B: In \( R \)
- Option C: In \( R \)
- Option D: Not in \( R \)

Thus, the correct answers are **Option B** and **Option C**.