# Category:Relation Theory

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This category contains results about Relation Theory.

Definitions specific to this category can be found in Definitions/Relation Theory.

**Relation theory** is the subfield of set theory concerned with the properties of relations and relational structures.

As a relation has the same conceptual definition as a (graph-theoretical) graph, it follows that there is considerable overlap between the fields of relation theory and graph theory.

## Subcategories

This category has the following 42 subcategories, out of 42 total.

### A

### C

### E

### F

### G

### H

### I

### L

### M

### O

### P

### R

### S

### T

## Pages in category "Relation Theory"

The following 64 pages are in this category, out of 64 total.

### C

### D

### E

### I

- Image is Subset of Codomain
- Image is Subset of Codomain/Corollary 1
- Image of Domain of Relation is Image Set
- Image of Element is Subset
- Image of Empty Set is Empty Set
- Image of Intersection under One-to-Many Relation
- Image of Intersection under One-to-Many Relation/Family of Sets
- Image of Intersection under One-to-Many Relation/General Result
- Image of Intersection under Relation
- Image of Intersection under Relation/Family of Sets
- Image of Intersection under Relation/General Result
- Image of Relation is Domain of Inverse Relation
- Image of Set Difference under Relation
- Image of Set Difference under Relation/Corollary 1
- Image of Set Difference under Relation/Corollary 2
- Image of Singleton under Relation
- Image of Subset under Relation equals Union of Images of Elements
- Image of Subset under Relation is Subset of Image
- Image of Subset under Relation is Subset of Image/Corollary 1
- Image of Union under Relation
- Image Preserves Subsets
- Image under Subset of Relation is Subset of Image under Relation
- Intersection of Relations is Relation
- Inverse Image under Embedding of Image under Relation of Image of Point

### M

### O

### P

### R

### S

### U

- Union of Left-Total Relations is Left-Total
- Union of Many-to-One Relations with Disjoint Domains is Many-to-One
- Union of One-to-Many Relations with Disjoint Images is One-to-Many
- Union of Relations is Relation
- Union of Right-Total Relations is Right-Total
- Union of Union of Relation is Union of Domain with Image
- Uniqueness Condition for Relation Value