You’ve just shown that $\langle x,y\rangle\in R$ if and only if $x=y$. In other words, $R$ is just the relation of equality on $\Bbb R$. This is a standard example of a relation that **is** reflexive: for each $x\in\Bbb R$, $x=x$, so $\langle x,x\rangle\in R$.
The other two properties that need to be checked are antisymmetry and transitivity.
* **Antisymmetry:** Is it true that if $\langle x,y\rangle\in R$ and $\langle y,x\rangle\in R$, then $x=y$?
* **Transitivity:** Is it true that if $\langle x,y\rangle\in R$ and $\langle y,z\rangle\in R$, then $\langle x,z\rangle\in R$?
In both cases you should begin by translating statments like $\langle x,y\rangle\in R$ into more basic statements about $x$ and $y$ by using the definition of $R$. For instance, we’ve already seen that $\langle x,y\rangle\in R$ means simply that $x=y$.