Question

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

Answer 1

We have,

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

For the elements of the given set A, we find that

$|1^2-1^2|\le 5,|2^2-2^2|\le 5,|3^2-3^2|\le 5,|1^2-1^2|\le 5,|2^2-1^2|\le 5,|2^2-3^2|\le 5,$ and $|3^2-2^2|\le 5,$

$\Rightarrow R=\left\{\right(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2\left)\right\}$