# Category:Transitive Relations

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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.

## Pages in category "Transitive Relations"

The following 35 pages are in this category, out of 35 total.

### A

### C

### I

### M

### R

- Reflexive and Symmetric Relation is not necessarily Transitive
- Reflexive and Transitive Relation is Idempotent
- Reflexive and Transitive Relation is not necessarily Symmetric
- Reflexive Closure of Transitive Antisymmetric Relation is Ordering
- Reflexive Relation on Set of Cardinality 2 is Transitive
- Relation Induced by Strict Positivity Property is Transitive
- Relation Isomorphism Preserves Transitivity
- Relation on Set of Cardinality 1 is Symmetric and Transitive
- Relations with Combinations of Reflexivity, Symmetry and Transitivity Properties
- Restriction of Transitive Relation is Transitive