Partial Order Relation

Partial Order Relation

## Definition / Concept

A relation is a partial order relation if it is reflexive, anti-symmetric and transitive.

## Formula

$$R\text{ is a partial order}\Leftrightarrow R\text{ is reflexive, anti-symmetric and transitive}$$

## Conditions / Special Cases

Reflexivity:

$$aRa\quad\forall a\in A$$

Anti-symmetry:

$$aRb,\ bRa\Rightarrow a=b$$

Transitivity:

$$aRb,\ bRc\Rightarrow aRc$$

## Terminologies

- Partially ordered set / Poset → A set together with a partial order relation.

## Usage

- Used in problems involving divisibility and subset relations.