Question

Let A = {1, 2, 3, 4} and R = {(a, b) : $aϵA,bϵA,$ a divides b} Write R explicity.

Answer 1

We have,

A = {1, 2, 3, 4}

and, R = {(a, b) = $aϵA,bϵA,$ a divides b}

Now,

$\frac{a}{b}$ stands for 'a divides b'. For the elements of the given sets, we find that $\frac{1}{1}$, $\frac{1}{2}$, $\frac{1}{3}$, $\frac{1}{4}$, $\frac{2}{2}$, $\frac{3}{3}$ and $\frac{4}{4}$

$\therefore$ R = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2, 4), (3, 3), (4, 4)}