Question

Let \( R \) be the relation in the set \( \mathbb{N} \) given by \( R = \{(a,b) : a = b - 2, \; b<6\} \), then _____

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

Hint:

Always check both conditions in relation definition carefully.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
For an ordered pair $(a, b)$ to be in the relation $R$, it must satisfy two conditions: 1. $a = b - 2$ 2. $b<6$
Step 2: Formula Application:
Let's check the options:
(a) $(6, 8)$: $b = 8$, which is NOT less than 6.
(b) $(8, 7)$: $b = 7$, which is NOT less than 6.
(c) $(8, 3)$: $b = 3$ (Condition 2 passed), but $a = 3 - 2 = 1 \neq 8$.
(d) $(2, 4)$: $b = 4$ (Condition 2 passed) and $a = 4 - 2 = 2$ (Condition 1 passed).
Step 3: Explanation:
Only the pair $(2, 4)$ satisfies both the equality and the inequality constraint given in the set definition.
Step 4: Final Answer:
The correct option is (d).