Let A = {1, 2, 3} and R
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)}

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