 Union of equivalence relations

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.