Question

Let A = {1, 2, 3} and $R=\left\{\left(a,b\right):\left|a^2-b^2\right|\le 5,a,b\in A\right\}$. Then write R as set of ordered pairs.

Answer 1

Given:
A = {1, 2, 3}
$R=\left\{\left(a,b\right):\left|a^2-b^2\right|\le 5,a,b\in A\right\}$

We know that
$$\begin{gathered} \left|1^2-1^2\right|\le 5, \\ \left|2^2-2^2\right|\le 5, \\ \left|3^2-3^2\right|\le 5, \\ \left|1^2-2^2\right|\le 5, \\ \left|2^2-1^2\right|\le 5, \\ \left|2^2-3^2\right|\le 5, \\ \left|3^2-2^2\right|\le 5 \end{gathered}$$
Thus, R ={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}