Let A = {a, b, c}. A relation R on A is defined as R = {(a, a), (b, b), (a, b), (b, a)}. Which of the following is true?

Let A = {a, b, c}. A relation R on A is defined as R = {(a, a), (b, b), (a, b), (b, a)}. Which of the following is true?

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

Answer: C) R is symmetric and transitive

Explanation: (c, c) ∉ R → not reflexive. It is symmetric: (a, b) and (b, a) are present. Transitive: (a, b) and (b, a) → (a, a) ∈ R; (b, a) and (a, b) → (b, b) ∈ R. So R is symmetric and transitive but not reflexive.