# Thread: Union of Transitive Relations

1. ## Union of Transitive Relations

What would a counterexample look like to prove the union of two transitive relations on the same set need not be transitive?

2. On the set $\left\{ {a,e,i,o,u} \right\}$ both $R = \left\{ {\left( {a,e} \right)} \right\}\,\& \,S\left\{ {\left( {e,i} \right)} \right\}$ are transitive.