Question

Let $R$ be a relation on the set of natural numbers $N$ defined by $xRy$ iff $2x+3y=21.$ Then $R$ is

• A. reflexive
• B. symmetric
• C. transitive
• D. None of these

Answer 1

The correct option is D None of these

$2x+3y=21$

$\left(i\right)$ Reflexive :
Let $xRx$
$\Rightarrow 2x+3x=21$
$\Rightarrow 5x=21\Rightarrow x=\frac{21}{5}\notin N$
$\therefore R$ is not reflexive.

$\left(ii\right)$ Symmetric :
Let $xRy$
$\Rightarrow 2x+3y=21$
$(9,1)\in R$ but $(1,9)\notin R$
$\therefore R$ is not symmetric.

$\left(iii\right)$ Transitive :
$(6,3),(3,5)\in R$ but $(6,5)\notin R$
$\therefore R$ is not transitive.