Let A={1,2,3} . Then find the number of relations containing (1,2) and (1, 3) which are reflexive and symmetric but not transitive.

Let relation R be reflexive, symmetric but not transitive containing (1,2) and (1, 3). Since R is reflexive, we must have (1,1),(2,2) and (3,3)∈RSince R is symmetric, we must have (2,1),(3,1)∈RNow, if we add one of the two pairs (3, 2) and (2, 3) (or both) to relation R, then relation R will become transitive. Hence, the total number of desired relations is 1.