# Category:Transitive Relations

This category contains results about Transitive Relations.
Definitions specific to this category can be found in Definitions/Transitive Relations.

$\RR$ is transitive if and only if:

$\tuple {x, y} \in \RR \land \tuple {y, z} \in \RR \implies \tuple {x, z} \in \RR$

that is:

$\set {\tuple {x, y}, \tuple {y, z} } \subseteq \RR \implies \tuple {x, z} \in \RR$

## Subcategories

This category has the following 12 subcategories, out of 12 total.