question_answer 72)

Let A = {1, 2, 3}, Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is (a) 1 (b) 2 (c) 3 (d) 4  

Answer:

Let a relation R is defined as       R = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1), (3, 3)}       As (1, 1), (2, 3), (3, 3) belongs to R.              is reflexive.       and (1, 2), (2, 1), (1, 3) and (3, 1) belongs to R.              is not transitive       is correct.