# Math Help - Equality

1. ## Equality

Prove that equality is the smallest equilivence relation on a set A.

2. Originally Posted by Chris11
Prove that equality is the smallest equilivence relation on a set A.
Given a set $A$ then $\Delta _A = \left\{ {(x,x):x \in A} \right\}$ is known as the diagonal.
Also $\Delta _A$ is also the equality relation.
Also if $\mathcal{E}$ is an equivalence on $A$ then it must be the case that $\Delta_A\subseteq\mathcal{E}$.