# Prove that relation R defined on the set N of natural numbers by $x\;R\;y \Leftrightarrow 2x^2-3xy+y^2=0$ is not symmetric but it is reflexive.

Suppose xRy implies 2x^2−3xy+y^2=0 2x^2-(x^2)−3xy+y^2+y^2=y^2-x^2 x^2−3xy+2y^2=y^2-x^2 x^2−3xy+2y^2=0 iff y^2-x^2=0 i.e, yRx Iff y^2=x^2 Iff. Y=+x or -x But y is inN implies that y=x, ie reflexive