Q130 / 240 · KCET 2026 · Mathematics
Let R be the relation in the set $\mathbb{N}$ given by $R = \{(a, b) : a = b - 2, b > 6\}$. Which of the following is the correct answer?
- A$(2, 4) \in R$
- B$(3, 8) \in R$
- Correct answerC$(6, 8) \in R$
- D$(8, 7) \in R$
Solution
Given relation $R = \{(a, b) : a = b - 2, b > 6\}$ on the set of natural numbers $\mathbb{N}$.
For $(2, 4)$, $b = 4$ which is not greater than $6$. Thus, $(2, 4) \notin R$.
For $(3, 8)$, $b = 8 > 6$ but $a = 3 \neq 8 - 2$. Thus, $(3, 8) \notin R$.
For $(6, 8)$, $b = 8 > 6$ and $a = 6 = 8 - 2$. Thus, $(6, 8) \in R$.
For $(8, 7)$, $b = 7 > 6$ but $a = 8 \neq 7 - 2$. Thus, $(8, 7) \notin R$.
Answer: $(6, 8) \in R$
For $(2, 4)$, $b = 4$ which is not greater than $6$. Thus, $(2, 4) \notin R$.
For $(3, 8)$, $b = 8 > 6$ but $a = 3 \neq 8 - 2$. Thus, $(3, 8) \notin R$.
For $(6, 8)$, $b = 8 > 6$ and $a = 6 = 8 - 2$. Thus, $(6, 8) \in R$.
For $(8, 7)$, $b = 7 > 6$ but $a = 8 \neq 7 - 2$. Thus, $(8, 7) \notin R$.
Answer: $(6, 8) \in R$
Hence, the correct answer is option: 'C'.