Question

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

Answer 1

A relation $R$ from the set $A=\{2,3,4,5\}$ to $B=\{3,6,7,10\}$ is defined as, $(x,y)\in R\Rightarrow x$ is relatively prime to $y$.

Now, it is seen that $2$ is relatively prime to $3$, [HCF of $2$ and $3$ is $1$]

So, $(2,3)\in R$

Similarly, $2$ is relatively prime to $7$ so that $(2,7)\in R$ etc.

So, we get $R=\{(2,3),(2,7),(3,7),(3,10),(4,3),(4,7),(5,3),(5,6),(5,7)\}$

Thus, domain $=\{2,3,4,5\}$ and range $=\{3,6,7,10\}$.