Question

Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.

Answer 1

No, it is not true.

Consider a set A = {1, 2, 3} and relation R on A such that R = {(1, 2), (2, 1), (2, 3), (1, 3)}
The relation R on A is symmetric and transitive. However, it is not reflexive.

$\left(1,1\right),\left(2,2\right)\mathrm{and}\left(3,3\right)\notin R$

Hence, R is not reflexive.