The relation I am looking at is $\{(0,0),(1,1),(1,3),(2,2),(2,3),(3,1),(3,2),(3,3)\}$, and is on the set $\{0,1,2,3\}$
Apparently, the only thing that does not qualify this as an equivalence relation is the fact that it is not transitive. However, I can not see this.
I tried to work it out: $1R3\wedge3R1 \rightarrow 1R1$ True
$2R3\wedge3R2 \rightarrow 2R2$ True
I didn't feel it was necessary to show things like, $0R0\wedge0R0\rightarrow0R0$