The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(x, y)…

We have  R = $\left\{(x, y):\left|x^2-y^2\right|<16\right\}$

Let x = 1  ∴ $\left|x^2-y^2\right|<16 \Rightarrow \left|1-y^2\right|<16$

$\Rightarrow \left|y^2-1\right|<16 \Rightarrow y=1,2,3,4$

Let y = 2  ∴ $\left|x^2-y^2\right|<16 \Rightarrow \left|4-y^2\right|<16$

$\Rightarrow \left|y^2-4\right|<16 \Rightarrow y=1,2,3,4$

Let y = 3  ∴ $\left|x^2-y^2\right|<16 \Rightarrow \left|9-y^2\right|<16$

$\Rightarrow \left|y^2-9\right|<16 \Rightarrow y=1,2,3,4$

Let y = 4  ∴ $\left|x^2-y^2\right|<16 \Rightarrow \left|16-y^2\right|<16$

$\Rightarrow \left|y^2-16\right|<16 \Rightarrow y=1,2,3,4,5$

Let y = 5  ∴ $\left|x^2-y^2\right|<16 \Rightarrow \left|25-y^2\right|<16$

$\Rightarrow \left|y^2-25\right|<16 \Rightarrow y=4,5$

∴ R {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (4, 4), (4, 5), (5, 4), (5, 5)}.

∴ The correct answer is (4).

Hence (4) is the correct answer.