$$R_3 = \{(x,y) \in \mathbb{Z} \times \mathbb{Z}|\frac{x-y}{5} \in \mathbb{Z}\} $$ $$R_4 = \{(x,y) \in \mathbb{Z} \times \mathbb{Z}|x > y \} $$
I need to know which one is reflexive, symmetric, antisymmetric, transitive and if they're an equivalence relation, what are their equivalence classes?
For now, I think $R_3$ and $R_4$ are antisymetric, but I don't know if there're reflexive or transitive.
And, I don't know if I'm right to think that.