# Category:Inverse Relations

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This category contains results about Inverse Relations.

Let $\mathcal R \subseteq S \times T$ be a relation.

The **inverse relation to** (or **of**) $\mathcal R$ is defined as:

- $\mathcal R^{-1} := \set {\tuple {t, s}: \tuple {s, t} \in \mathcal R}$

## Subcategories

This category has only the following subcategory.

### I

## Pages in category "Inverse Relations"

The following 37 pages are in this category, out of 37 total.

### I

- Image of Relation is Domain of Inverse Relation
- Intersection of Relation with Inverse is Symmetric Relation
- Inverse of Antireflexive Relation is Antireflexive
- Inverse of Antisymmetric Relation is Antisymmetric
- Inverse of Antitransitive Relation is Antitransitive
- Inverse of Asymmetric Relation is Asymmetric
- Inverse of Composite Relation
- Inverse of Injection is Many-to-One Relation
- Inverse of Injection is One-to-One Relation
- Inverse of Inverse Relation
- Inverse of Left-Total Relation is Right-Total
- Inverse of Many-to-One Relation is One-to-Many
- Inverse of Mapping is One-to-Many Relation
- Inverse of Mapping is Right-Total Relation
- Inverse of Non-Reflexive Relation is Non-Reflexive
- Inverse of Non-Symmetric Relation is Non-Symmetric
- Inverse of Non-Transitive Relation is Non-Transitive
- Inverse of One-to-One Relation is One-to-One
- Inverse of Reflexive Relation is Reflexive
- Inverse of Right-Total Relation is Left-Total
- Inverse of Subset of Relation is Subset of Inverse
- Inverse of Surjection is Relation both Left-Total and Right-Total
- Inverse of Symmetric Relation is Symmetric
- Inverse of Transitive Relation is Transitive
- Inverse Relation Equal iff Subset
- Inverse Relation is Left and Right Inverse iff Bijection
- Inverse Relation Properties
- Inverses of Right-Total and Left-Total Relations