Let R be the relation in the set N given by `R = {(a , b) : a = b-2, b > 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`

Explanation

To solve the problem, we need to analyze the relation \( R = \{(a, b) : a = b - 2, b > 6\} \) and determine which of the given options belongs to this relation.

### Step 1: Understand the Relation
The relation states that for any pair \( (a, b) \) to be in \( R \):
- \( a \) must equal \( b - 2 \)
- \( b \) must be greater than 6

### Step 2: Evaluate Each Option

**Option (A): (2, 4)**
- Here, \( a = 2 \) and \( b = 4 \).
- Check if \( b > 6 \): \( 4 > 6 \) is **false**.
- Since \( b \) does not satisfy the condition, **(2, 4) is not in R**.

**Option (B): (3, 8)**
- Here, \( a = 3 \) and \( b = 8 \).
- Check if \( b > 6 \): \( 8 > 6 \) is **true**.
- Now check if \( a = b - 2 \): \( 3 = 8 - 2 \) gives \( 3 = 6 \), which is **false**.
- Therefore, **(3, 8) is not in R**.

**Option (C): (6, 8)**
- Here, \( a = 6 \) and \( b = 8 \).
- Check if \( b > 6 \): \( 8 > 6 \) is **true**.
- Now check if \( a = b - 2 \): \( 6 = 8 - 2 \) gives \( 6 = 6 \), which is **true**.
- Thus, **(6, 8) is in R**.

**Option (D): (8, 7)**
- Here, \( a = 8 \) and \( b = 7 \).
- Check if \( b > 6 \): \( 7 > 6 \) is **true**.
- Now check if \( a = b - 2 \): \( 8 = 7 - 2 \) gives \( 8 = 5 \), which is **false**.
- Therefore, **(8, 7) is not in R**.

### Conclusion
The only pair that satisfies both conditions of the relation \( R \) is **(6, 8)**. Therefore, the correct answer is **(C) (6, 8) in R**.