Preorder Relation

Last updated Nov 1, 2022

Let $P$ be a Set and let $R \subset P \times P$ be a Relation on $P$. Then $R$ is a Preorder Relation if

1. Reflexitivity: $xRx$ for all $x \in P$
2. Transitivity: Let $x,y,z \in P$. If $xRy$ and $yRz$ then $xRz$