For  $x,y\in R$, define a relation R by xRy if and only if $2x-2y+\sqrt{3}$ is an irrational number then R is 

S-I: Since $2x-2x+\sqrt{3}=\sqrt{3}$ is an irrational number so $xRx\Rightarrow R$ is reflexive.
Here $(\frac{\sqrt{3}}{2},1)\in R$, but $(1,\frac{\sqrt{3}}{2})\notin R$,
So R is not symmetric, not Transitive