# Category:Reflexive Relations

This category contains results about Reflexive Relations.

$\mathcal R$ is **reflexive** if and only if:

- $\forall x \in S: \tuple {x, x} \in \mathcal R$

## Also see

## Subcategories

This category has the following 7 subcategories, out of 7 total.

### E

### R

## Pages in category "Reflexive Relations"

The following 40 pages are in this category, out of 40 total.

### A

### E

### I

### R

- Reflexive and Symmetric Relation is not necessarily Transitive
- Reflexive and Transitive Relation is Idempotent
- Reflexive and Transitive Relation is not necessarily Symmetric
- Reflexive Circular Relation is Equivalence
- Reflexive Euclidean Relation is Equivalence
- Reflexive Relation is Serial
- Reflexive Relation on Set of Cardinality 2 is Transitive
- Relation is Antireflexive iff Disjoint from Diagonal Relation
- Relation is Antisymmetric and Reflexive iff Intersection with Inverse equals Diagonal Relation
- Relation is Connected and Reflexive iff Total
- Relation is Reflexive and Coreflexive iff Diagonal
- Relation is Symmetric and Antisymmetric iff Coreflexive
- Relation Isomorphism Preserves Reflexivity
- Relation Reflexivity
- Relations with Combinations of Reflexivity, Symmetry and Transitivity Properties
- Restriction of Antireflexive Relation is Antireflexive
- Restriction of Non-Reflexive Relation is Not Necessarily Non-Reflexive
- Restriction of Reflexive Relation is Reflexive