Question

Let R be the relation in the set N given by $R = \{(a, b) : a = b - 2, b>6\}$. Which of the following is the correct answer?

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

Hint:

Always test the easiest or most restrictive condition first. By simply looking for pairs where the second number $b$ is greater than 6, you immediately eliminate option (1) without any calculation. Then apply the equation test.

Answer 1

The Correct Option is C

Step 1: Given Relation
\[ R = \{(a, b) : a = b - 2,\; b>6\} \] 
Step 2: Conditions to Check 
For any ordered pair $(a,b)$ to belong to $R$, it must satisfy:

• $a = b - 2$
• $b>6$

Step 3: Verify Each Option 
(1) $(2,4)$ 
\[ b = 4 \not> 6 \Rightarrow \text{Not in } R \] (2) $(3,8)$ 
\[ 8>6 \ (\text{true}), 3 \neq 8 - 2 = 6 \] \[ \Rightarrow \text{Not in } R \] (3) $(6,8)$ 
\[ 8>6 \ (\text{true}), 6 = 8 - 2 \] \[ \Rightarrow (6,8) \in R \] (4) $(8,7)$ 
\[ 7>6 \ (\text{true}), 8 \neq 7 - 2 = 5 \] \[ \Rightarrow \text{Not in } R \] 
Step 4: Final Answer 
\[ \boxed{(6, 8) \in R} \]