Empty Relation

Empty Relation

## Definition / Concept

The empty relation contains no ordered pair.

## Formula

$$R=\varnothing$$

## Conditions / Special Cases

For a non-empty set $A$, the empty relation is symmetric and transitive but not reflexive.

Therefore:

$$R=\varnothing\Rightarrow R\text{ is not an equivalence relation for }A\ne\varnothing$$

## Usage

- Used as a standard counterexample when checking reflexivity.