# Let R be the relation in the set N given by R = {(a, b): a = b − 2, b > 6}.

Question:

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

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

Solution:

$\mathrm{R}=\{(a, b): a=b-2, b>6\}$

Now, since $b>6,(2,4) \notin \mathrm{R}$

Also, as $3 \neq 8-2,(3,8) \notin \mathrm{R}$

And, as $8 \neq 7-2$

$\therefore(8,7) \notin \mathrm{R}$

Now, consider $(6,8)$.

We have $8>6$ and also, $6=8-2$.

$\therefore(6,8) \in \mathrm{R}$

The correct answer is $C$.