The relation R defined in A = {1, 2, 3} by aRb if $\left|{\mathrm{a}}^2-{\mathrm{b}}^2\right|\le 5$. Which of the following is false

Let $\mathrm{a}=1\therefore {\mathrm{a}}^2-{\mathrm{b}}^2\mathrm{l}\le 5\Rightarrow 1-{\mathrm{b}}^2\mid \le 5$
$\begin{array}{l}\Rightarrow \mid {\mathrm{b}}^2-1\mathrm{I}\le 5\Rightarrow \mathrm{b}=1,2\\ \text{ Let }\mathrm{a}=2\therefore \left|{\mathrm{a}}^2-{\mathrm{b}}^2\le 5\Rightarrow \right|4-{\mathrm{b}}^2\mid \le 5\\ \text{ Let }3\therefore \left|{\mathrm{a}}^2-{\mathrm{b}}^2\right|\le 5\Rightarrow \mid 9-{\mathrm{b}}^2\le 5\\ \Rightarrow \left|{\mathrm{b}}^2-9\right|\le 5\Rightarrow \mathrm{b}=2,3\\ \therefore \mathrm{R}=\left\{\right(1,1),(1,2),(2,1),(2,2\left)\right(2,3),(3,2\left)\right(3,3\left)\right\}\\ {\mathrm{R}}^{-1}=\left\{\right(\mathrm{y},\mathrm{x}):(\mathrm{x},\mathrm{y})\in \mathrm{R}\}\\ \Rightarrow R=\left\{\right(1,1),(2,1),(1,2),(2,2\left)\right(3,2),(2,3\left)\right(3,3\left)\right\}\end{array}$
Domain of $\mathrm{R}=\{\mathrm{x}:(\mathrm{x},\mathrm{y})\in \mathrm{R}\}=\{1,2,3\}$
$\Rightarrow$Range of $\mathrm{R}=\{\mathrm{y}:(\mathrm{x},\mathrm{y})\in \mathrm{R}\}=\{1,2,3\}$