Question

Let $A=\{6,8\},$ $B=\{1,3,5\}$ and $R=\left\{\right(a,b):a\in A,b\in B,a-biseven\}$.
Show that R is an empty relation from A to B.

Answer 1

Given, $A=\{6,8\}$ and $B=\{1,3,5\}$

Thus, every element $a\in A$ is an even number and every element $b\in B$ is an odd number

So, $(a-b)$ will be an odd number

Thus, there is no pair $(a,b)$ such that $(a-b)$ is even

Therefore, $R$ is an empty relation.