Question

What is the final classification of the relation \(aRb\) on the real numbers defined by \(a-b<5\)?

Options

• It is an equivalence relation

• It is symmetric and transitive but not reflexive

• It is reflexive, symmetric, and transitive

• It is not an equivalence relation

Answer 1

Although the relation is reflexive, the examples show that it is neither symmetric nor transitive. Since all three properties are required, it is not an equivalence relation.