Question

A relation \( R = \{(a, b) : a = b - 2, b \geq 6 \} \) is defined on the set \( \mathbb{N} \). Then the correct answer will be:

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

Hint:

To verify a relation, check both the defining equation and the additional constraints for all given pairs.

Answer 1

The Correct Option is C

The given relation is \( R = \{(a, b) : a = b - 2, b \geq 6\} \). 
For each pair: 
For \( (2, 4) \): \( a = 4 - 2 = 2 \) and \( b = 4 \). 
Since \( b \geq 6 \) is not satisfied, \( (2, 4) \notin R \). 
For \( (3, 8) \): \( a = 8 - 2 = 6 \) and \( b = 8 \). Since \( a \neq 3 \), \( (3, 8) \notin R \).  
For \( (6, 8) \): \( a = 8 - 2 = 6 \) and \( b = 8 \). 
Both conditions \( a = b - 2 \) and \( b \geq 6 \) are satisfied, so \( (6, 8) \in R \). 
For \( (8, 7) \): \( a = 7 - 2 = 5 \) and \( b = 7 \). 
Since \( a \neq 8 \), \( (8, 7) \notin R \). 
Thus, the correct pair is \( (6, 8) \).