Union of equivalence relations
= Union of equivalence relations
{title2=$R\cup S$}
A union of <equivalence relations> on the same <set> is reflexive and symmetric, but can fail <transitivity>. On a three-point <set>, partitions into blocks $\{1,2\},\{3\}$ and $\{1\},\{2,3\}$ make the union relate $1$ to $2$ and $2$ to $3$ without relating $1$ to $3$. An equivalence relation containing both requires transitive closure as well.