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 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.
$(1,1),(2,2)$ and $(3,3) \notin R$
Hence, R is not reflexive.