Universal Relation

Universal Relation

## Definition / Concept

The universal relation on $A$ contains every ordered pair in $A\times A$.

## Formula

$$R=A\times A$$

If:

$$n(A)=n$$

then:

$$n(R)=n^2$$

## Conditions / Special Cases

The universal relation is reflexive, symmetric and transitive.

Therefore:

$$R\text{ is an equivalence relation}$$

## Usage

- Used as an extreme case while classifying relations.