Union of Equivalences/Proof 2

Theorem

The union of two equivalence relations is not necessarily an equivalence relation itself.

Proof

We have that the Union of Reflexive Relations is Reflexive.

We also have that the Union of Symmetric Relations is Symmetric.

However, we also have that the Union of Transitive Relations Not Always Transitive.

Hence the union of two equivalence relations is not always an equivalence relation.

$\blacksquare$