If a relation R on the set {1, 2, 3} is defined by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}, then R is:

If a relation R on the set {1, 2, 3} is defined by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}, then 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: Contains all (a, a) → reflexive. Symmetric because (1, 2) and (2, 1) are both present. Transitive: (1, 2) and (2, 1) → (1, 1) ∈ R; (2, 1) and (1, 2) → (2, 2) ∈ R. All conditions satisfied, so it is an equivalence relation.