Question

A relation R is defined from a set A = {2, 3, 4, 5} to a set B = {3, 6, 7, 10} as follows : $\{x,y\}ϵR\iff x$ is relatively prime to y. Express R as a set of ordered pairs and determine its domain and range.

Answer 1

We have

A = {2, 3, 4, 5} and B = {3, 6, 7, 10} It is given that $x,yϵR\iff x$ is relatively prime to y

$\therefore (2,3)ϵR,(2,7)ϵR,(3,7)ϵR,(3,10)ϵR,(4,3)ϵR,(4,7)ϵR,(5,3)ϵR,$ and $(5,7)ϵR$

Thus,

R = {(2, 3), (2, 7), (3, 7), (3, 10), (4, 3), (4, 7), (5, 3), (5, 7)}

Clearly, Domain (R) = {2, 3, 4, 5} and Range = {3, 7, 10}