On $\Bbb Z$ consider the relation $xRy \Leftrightarrow x-y \not\equiv 0 \mod 3$.
Prove (with explanation), whether the relation reflexive, symmetric, antisymmetric transitive is and prove if they are equivalence relation or order relation
I have computed:
1) Reflexive NO
2) Symmetric YES
3) Antisymmetric NO (I'm not sure here)
4) Transitive YES ( I'm not sure here as well)
Is this a good solution? If not, can you explain where the mistake is?