Let R = {(a, b) : a, b ∈ Z, a − b is divisible by 5}. R is:

Let R = {(a, b) : a, b ∈ Z, a − b is divisible by 5}. R is:

• A. reflexive and symmetric but not transitive
• B. reflexive and transitive but not symmetric
• C. symmetric and transitive but not reflexive
• D. an equivalence relation

Answer: D) an equivalence relation

Explanation: a − a = 0 divisible by 5 → reflexive. If a − b = 5k then b − a = −5k divisible by 5 → symmetric. If a − b = 5k and b − c = 5m then a − c = 5(k+m) → transitive. Hence equivalence relation.