Let L denote the set of all straight lines in a plane . Let a relation R defined on L by $\mathrm{XRY}\iff \mathrm{X}\perp \mathrm{Y};\mathrm{X},\mathrm{Y}\in \mathrm{L}\text{ then }\mathrm{R}$ is 

Clearly, R is not a reflexive relation because a line con not be perpendicular to itself
Let ${\mathrm{X}}_1{\mathrm{RY}}_1\text{ then }{\mathrm{X}}_1\perp {\mathrm{Y}}_1\Rightarrow {\mathrm{Y}}_1\perp {\mathrm{X}}_1 \mathrm{hence} {\mathrm{Y}}_1{\mathrm{RX}}_1$

$\therefore$R is symmetric.
$\therefore$ R is not a transition relation because if ${\mathrm{X}}_1\perp {\mathrm{Y}}_1$ and ${\mathrm{Y}}_1\perp {\mathrm{Z}}_1\text{ then }{\mathrm{X}}_1\text{ not perpendicular to }{\mathrm{Z}}_1$