Solution
= Solution
On the nonempty <set> $X=\{a\}$ take the empty <binary relation> $R=\varnothing$. There are no triples for which $xRy\land xRz$ holds. The defining implication is therefore true for every triple by <vacuous truth>, making $R$ a <Euclidean relation>.
But $aRa$ is false, so $R$ is not a <reflexive relation> and hence is not an <equivalence relation>:
$$
\boxed{(X,R)=(\{a\},\varnothing)\text{ is a counterexample}.}
$$