# Category:Symmetric Relations

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This category contains results about **Symmetric Relations**.

$\RR$ is **symmetric** if and only if:

- $\tuple {x, y} \in \RR \implies \tuple {y, x} \in \RR$

## Subcategories

This category has the following 9 subcategories, out of 9 total.

## Pages in category "Symmetric Relations"

The following 33 pages are in this category, out of 33 total.

### C

### I

### R

- Reflexive and Symmetric Relation is not necessarily Transitive
- Reflexive and Transitive Relation is not necessarily Symmetric
- Relation both Symmetric and Asymmetric is Null
- Relation equals Inverse iff Symmetric
- Relation Intersection Inverse is Greatest Symmetric Subset of Relation
- Relation is Reflexive Symmetric and Antisymmetric iff Diagonal Relation
- Relation is Symmetric and Antisymmetric iff Coreflexive
- Relation is Symmetric iff Inverse is Symmetric
- Relation Isomorphism Preserves Symmetry
- Relation on Set of Cardinality 1 is Symmetric and Transitive
- Relation Symmetry
- Relations with Combinations of Reflexivity, Symmetry and Transitivity Properties
- Restriction of Symmetric Relation is Symmetric

### S

- Set Equivalence behaves like Equivalence Relation/Symmetric
- Symmetric and Antisymmetric Relation is Transitive
- Symmetric and Transitive Relation is not necessarily Reflexive
- Symmetric Preordering is Equivalence Relation
- Symmetric Relation equals its Symmetric Closure
- Symmetric Transitive and Serial Relation is Reflexive
- Symmetry of Relations is Symmetric