Question

The relation $x{y}^2$ $=x^{2}y$ defined on set of real numbers is

• A. reflexive and symmetric
• B. symmetric and transitive
• C. reflexive and transitive
• D. equivalence

Answer 1

The correct option is A reflexive and symmetric

$\left(i\right)x.x^2=x^2.x\Rightarrow xRx\Rightarrow$ Reflexive
$\left(ii\right)xRy\Rightarrow x{y}^2=x^{2}y\Rightarrow y^{2}x=y{x}^2\Rightarrow y{x}^2=y^{2}x\Rightarrow yRx$ $\Rightarrow$ Symmetric
$\left(iii\right)(1,0)\in R$ and $(0,2)\in R$ but $(1,2)\notin R$ so it's not Transitive