# Deciding If A Relation On A Set Is An Equivalence Relation

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, $0R0\wedge0R0\rightarrow0R0$

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For it to be transitive it has to satisfy $aRb \wedge bRc \Rightarrow aRc$ for ALL $a, b, c$ in the set that the relation $R$ is defined on. See if you can find one example where this isn't satisfied. –  Sam Jones Nov 8 '12 at 14:49

$1R3$ and $3R2$ but not $1R2$.