1. **Problem:** Define an empty relation. 2. **Definition:** A relation $R$ on a set $A$ is a subset of the Cartesian product $A \times A$. 3. **Empty Relation:** An empty relation on $A$ is the relation $R = \emptyset$, meaning it contains no ordered pairs. 4. **Explanation:** Since $R$ has no elements, it relates no elements of $A$ to any other elements. 5. **Summary:** The empty relation is simply the relation with no pairs, i.e., $R = \emptyset$. Final answer: An empty relation is a relation that contains no ordered pairs, i.e., $R = \emptyset$.