Consider set A = {1, 2, 3}. Number of relations that can be defined on A containing the ordered pair (1, 2) & (1, 3) which are reflexive & symmetric but not transitive

A={1,2,3}

Relation containing (1, 2) and (1, 3)

For symmetricity, (1,2),(2,1),(1,3) and (3,1) must be included.

For reflexivity, (1, 1), (2, 2), (3, 3) must be included.

⇒ Only one set is there
 R = {(1, 1), (1, 2), (1, 3), (2, 2), (2, 1), (3, 3), (3, 1)}