Question:
Let $\mathrm{A}=\{1,2,3\}$ and $R=\left\{(a, b):\left|a^{2}-b^{2}\right| \leq 5, a, b \in A\right\}$. Then write $\mathrm{R}$ as set of ordered pairs.
Solution:
Given:
A = {1, 2, 3}
$R=\left\{(a, b):\left|a^{2}-b^{2}\right| \leq 5, a, b \in A\right\}$
We know that
$\left|1^{2}-1^{2}\right| \leq 5$
$\left|2^{2}-2^{2}\right| \leq 5$
$\left|3^{2}-3^{2}\right| \leq 5$,
$\left|1^{2}-2^{2}\right| \leq 5$,
$\left|2^{2}-1^{2}\right| \leq 5$
$\left|2^{2}-3^{2}\right| \leq 5$
$\left|3^{2}-2^{2}\right| \leq 5$
Thus, R ={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}