# 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 7 subcategories, out of 7 total.

### E

### R

### S

## Pages in category "Symmetric Relations"

The following 55 pages are in this category, out of 55 total.

### A

### C

### E

### I

### R

- Reflexive and Symmetric Relation is not necessarily Transitive
- Reflexive and Transitive Relation is not necessarily Symmetric
- Reflexive Closure of Transitive Antisymmetric Relation is Ordering
- Relation both Symmetric and Asymmetric is Null
- Relation equals Inverse iff Symmetric
- Relation Intersection Inverse is Greatest Symmetric Subset of Relation
- Relation is Antisymmetric and Reflexive iff Intersection with Inverse equals Diagonal Relation
- Relation is Antisymmetric iff Intersection with Inverse is Coreflexive
- 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 Antisymmetry
- Relation Isomorphism Preserves Symmetry
- Relation on Set of Cardinality 1 is Symmetric and Transitive
- Relation on Set of Cardinality 2 cannot be Non-Symmetric and Non-Transitive
- Relation Symmetry
- Relations with Combinations of Reflexivity, Symmetry and Transitivity Properties
- Restriction of Antisymmetric Relation is Antisymmetric
- Restriction of Asymmetric Relation is Asymmetric
- Restriction of Non-Symmetric Relation is Not Necessarily Non-Symmetric
- Restriction of Symmetric Relation is Symmetric

### S

- Set Equivalence behaves like Equivalence Relation/Symmetric
- Strictly Well-Founded Relation is Asymmetric
- Symmetric and Antisymmetric Relation is Transitive
- Symmetric and Transitive Relation is not necessarily Reflexive
- Symmetric Closure of Symmetric Relation
- Symmetric Preordering is Equivalence Relation
- Symmetric Transitive and Serial Relation is Reflexive
- Symmetry of Relations is Symmetric