# Category:Composite Relations

Jump to navigation
Jump to search

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

Let $\RR_1 \subseteq S_1 \times T_1$ and $\RR_2 \subseteq S_2 \times T_2$ be relations.

Then the **composite of $\RR_1$ and $\RR_2$** is defined and denoted as:

- $\RR_2 \circ \RR_1 := \set {\tuple {x, z} \in S_1 \times T_2: \exists y \in S_2 \cap T_1: \tuple {x, y} \in \RR_1 \land \tuple {y, z} \in \RR_2}$

## Subcategories

This category has only the following subcategory.

## Pages in category "Composite Relations"

The following 23 pages are in this category, out of 23 total.

### C

- Codomain of Composite Relation
- Composite of Antisymmetric Relations is not necessarily Antisymmetric
- Composite of Connected Relation is not necessarily Connected
- Composite of Orderings is not necessarily Ordering
- Composite of Reflexive Relations is Reflexive
- Composite of Symmetric Relations is Symmetric
- Composite of Total Relations is Total
- Composite of Transitive Relations is not necessarily Transitive
- Composition of Direct Image Mappings of Relations
- Composition of Inverse Image Mappings of Mappings
- Composition of Mappings is Composition of Relations
- Composition of Relation with Inverse is Symmetric
- Composition of Relations is Associative
- Condition for Composite Relation with Inverse to be Identity