Consider the relation $R = \{(x, x) : x \in \mathbb{Z}\}$ on $\mathbb{Z}$. Is $R$ reflexive? Symmetric? Transitive? If a property does not hold, say why. What familiar relation is this?
I think all of these properties are satisfied so it's an equivalence relation. It has to be reflexive as $x\mathrel{R}x$ is true for all $x$ integers. I also think it is symmetric and transitive.
What familiar relation is this? I would say it's an equivalence relation but I think they are searching for a more precise answer. I was also thinking of saying it is the set of all integer coordinates in the $x$-$y$ plane, but I don't think this is correct.