Question

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Answer 1

(i) (1, 1), (2, 2), (3, 3) do not belong to relation R.

∴ R is not reflexive.

(ii) It is symmetric because (1, 2) and (2, 1) belong to R.

(iii) There are only two elements 1 and 2 in this relation and there is no third element c in it. ⇒ R is not transitive.