Definition 5.37

Let $E$ be a binary relation over a set $V$.

1. $E$ is a $\text{preorder}$, if $E$ is reflexive and transitive
2. $E$ is a $\text{partial order}$, if $E$ is reflexive, transitive and antisymmetric
3. $E$ is a $\text{linear order}$ or total $\text{order}$, if $E$ is reflexive, transitive, antisymmetric and total