The relation R defined in A = {1, 2, 3} by aRb if |a² − b²| ≤ 5. Which of the following is false?

Range of R = {5}

Let a = 1    ∴ $\left|a^2-b^2\right| \leq 5 ⇒\left|1-b^2\right| \leq 5$

$⇒\left|b^2-1\right| \leq 5 ⇒ b = 1, 2$

Let  ⇒ a = 2   ∴ $\left|a^2-b^2\right| \leq 5$

⇒ $\left|b^2-4\right| \leq 5$ ⇒ b = 1, 2, 3

Let $⇒ a=3 ∴\left|a^2-b^2\right| \leq 5 ⇒\left|9-b^2\right| \leq 5$

$⇒ a=3 ∴\left|a^2-b^2\right| \leq 5 ⇒\left|9-b^2\right| \leq 5$

∴ R = {(1, 1), (1, 2), (2, 1), (2, 2), (2, 3), (3, 3)}

= R

Domain of R = {x : (x, y) ∈ R} = {1, 2, 3}.

Range of R = {y : (x, y) ∈ R} = {1, 2, 3}.

Hence (4) is the correct answer.