Let R be the relation on R defined by aRb if a − b is rational. R is:

Let R be the relation on R defined by aRb if a − b is rational. R is:

• A. reflexive and symmetric only
• B. equivalence relation
• C. reflexive and transitive only
• D. symmetric and transitive only

Answer: B) equivalence relation

Explanation: a − a = 0 ∈ Q → reflexive. If a − b ∈ Q then b − a = −(a − b) ∈ Q → symmetric. If a − b ∈ Q and b − c ∈ Q then a − c = (a−b)+(b−c) ∈ Q → transitive. So equivalence relation.