Is $R=\{(x,y):x-y \in \mathbb{R}-\mathbb{Q}\ \forall x,y \in \mathbb{R}-\mathbb{Q}\}$ an Equivalence Relation
Reflexivity: Obviously it is not Reflexive since $x=\sqrt{2}$ and $y=\sqrt{2}$ and $\sqrt{2}-\sqrt{2}=0$ is rational
Symmetry: It is symmetric since $x-y$ irrational $\implies$ $y-x$ is Irrational
Transitive: Not transitive since $\sqrt{2}-\sqrt{5}$ is Irrational
and $\sqrt{5}-\sqrt{2}$ is irrational but $\sqrt{2}-\sqrt{2}$ is rational.
Hence $R$ is not an Equivalence Relation
Is this approach correct?