Question

Let A = {3, 5} and B = {7, 11}. Let $R=\left\{\right(a,b):aϵA,bϵB,a-b$ is odd}. Show that R is an empty relation from A into B.

Answer 1

We have,

A = {3, 5}, B = {7, 11}

and, R = {(a, b) : $aϵA,bϵB,a-b$ is odd}

For the elements of the given sets A and B, we find that 3 - 7 = - 4, 3 -11 = - 8, 5 - 7 = - 2 and 5 - 11 = - 6

$\therefore (3,7)\text{/}ϵR,(3,11)\text{/}ϵR,(5,7)\text{/}ϵR$ and $(5,11)\text{/}ϵR,$

Thus, R is an empty relation from A into B.