The Clowder Project

Here are some examples of composition of relations.

1. 1. Composing Less/Greater Than Equal With Greater/Less Than Equal Signs. We have
   $$\begin{array}{rl}\le \diamond \ge & ={\sim }_{\mathrm{triv}},\\ \ge \diamond \le & ={\sim }_{\mathrm{triv}}.\end{array}$$
2. 2. Composing Less/Greater Than Equal Signs With Less/Greater Than Equal Signs. We have
   $$\begin{array}{rl}\le \diamond \le & =\le ,\\ \ge \diamond \ge & =\ge .\end{array}$$