The Clowder Project

Here are some examples of composition of relations.

1. Composing Less/Greater Than Equal With Greater/Less Than Equal Signs. We have
   \begin{align*} \mathord {\leq }\mathbin {\diamond }\mathord {\geq } & = \sim _{\mathrm{triv}},\\ \mathord {\geq }\mathbin {\diamond }\mathord {\leq } & = \sim _{\mathrm{triv}}. \end{align*}
2. Composing Less/Greater Than Equal Signs With Less/Greater Than Equal Signs. We have
   \begin{align*} \mathord {\leq }\mathbin {\diamond }\mathord {\leq } & = \mathord {\leq },\\ \mathord {\geq }\mathbin {\diamond }\mathord {\geq } & = \mathord {\geq }. \end{align*}