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

Question:

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

Solution:

No, it is not true.

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

$(1,1),(2,2)$ and $(3,3) \notin R$

Hence, R is not reflexive.

Leave a comment

Close

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now