Question

A relation $R = \{(a, b) : a = b - 1, b > 4\}$ is defined on set $\mathbb{N}$, then correct answer will be:

• A. $(2, 4)$
• B. $(4, 5)$
• C. $(4, 6)$
• D. $(3, 5)$

Hint:

For a relation of the form $a = b - 1$ with $b > 4$, check that each pair satisfies both conditions.

Answer 1

The Correct Option is B

Step 1: Understanding the relation.
The relation is defined as $a = b - 1$ and $b > 4$. This means for every element $b > 4$, we will find the corresponding $a$ such that $a = b - 1$.

Step 2: Check each option.
- (A) $(2, 4)$: For $a = 2$, $b = 2 + 1 = 3$, but $b > 4$ is not satisfied. Hence, $(2, 4)$ is incorrect.
- (B) $(4, 5)$: For $a = 4$, $b = 4 + 1 = 5$, and $b > 4$ is satisfied. Hence, $(4, 5)$ is correct.
- (C) $(4, 6)$: For $a = 4$, $b = 4 + 1 = 5$, but $b = 6$ does not match the condition for $b = 5$ when $a = 4$. Hence, $(4, 6)$ is incorrect.
- (D) $(3, 5)$: For $a = 3$, $b = 3 + 1 = 4$, but $b > 4$ is not satisfied. Hence, $(3, 5)$ is incorrect.

Step 3: Conclusion.
The correct answer is (B) $(4, 5)$, as it satisfies both conditions $a = b - 1$ and $b > 4$.