Let A = {1, 2, 3} and R be a relation on A defined as R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is:

Let A = {1, 2, 3} and R be a relation on A defined as R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is:

• A. Reflexive, symmetric but not transitive
• B. Reflexive, transitive but not symmetric
• C. Symmetric, transitive but not reflexive
• D. An equivalence relation

Answer: B) Reflexive, transitive but not symmetric

Explanation: R contains (a,a) for all a in A, so it is reflexive. It has (1,2) and (2,3) leading to (1,3) which is also in R, so it is transitive. However, (1,2) is in R but (2,1) is not, so it is not symmetric.