Which relation on A={1,2,3} is transitive but not reflexive?

Correct answer: R={(1,1),(2,2),(1,2),(2,1)}

Direct answer: C. A relation is reflexive on A only when (1,1), (2,2), and (3,3) are all present. Option C omits (3,3), so it is not reflexive. To check transitivity, the pairs (1,2) and (2,1) require (1,1), which is present; (1,2) followed by (2,2) again gives (1,2); (2,1) followed by (1,2) gives (2,2), present; and the remaining compositions stay within the listed pairs. Thus C is transitive. Option A contains every diagonal pair and is therefore reflexive as well as transitive. Option B has (1,2) and (2,3) but lacks (1,3), so it is not transitive. Option D has (2,1) and (1,2) but lacks (2,2), so it is not transitive. Check reflexivity first, then test every composable two-step chain.