If a relation R is both symmetric and transitive, then R is reflexive. For this, Mr. X offers the following proof:
“From xRy, using symmetry we get yRx. Now because R is transitive xRy and yRx together imply xRx. Therefore, R is reflexive”.
Ex: empty relation(no ordered pairs).
@Anshul Shankar your example is not correct because it is not transitive (1,2),(2,1) are in R but (1,1) is not in R, also (2,3),(3,2) are in R but (2,2) is not in R.