Question

A relation $R$ is defined from $\left\{2,3,4,5\right\}$ to $\left\{3,6,7,10\right\}$ by $xRy\Rightarrow x$ is relatively prime to $y$. Then the domain of $R$ is

• A. $\left\{2,3,5\right\}$
• B. $\left\{3,5\right\}$
• C. $\left\{2,3,4\right\}$
• D. $\left\{2,3,4,5\right\}$

Answer 1

The correct option is D

$\left\{2,3,4,5\right\}$

Explanation for the correct option:

Step 1. it is defined as $(x,y)\in R\Rightarrow x$ is relatively prime to $y$

Given set $A=\left\{2,3,4,5\right\}$ to $B=\left\{3,6,7,10\right\}$

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

Step 2. $2$ is relatively prime to $7$

$\Rightarrow (2,7)\in R$

Therefore, we get

$R=\left\{(2,3),(2,7),(3,7),(3,10),(4,3),(4,7),(5,3),(5,6),(5,7),\right\}$

Thus the required domain is $\left\{2,3,4,5\right\}$

Hence, Option ‘D’ is Correct.