Let A=1, 2, 3, 4 and R be a relation in A given by R=1, 1, 2, 2, 3, 3, 4, 4, 1, 2, 2, 1, 3, 1, 1, 3.
Then R is
Reflexive
Symmetric
Transitive
An equivalence
1, 22, 23, 34, 4∈R; ∴R is reflexive.
∵1, 2 3, 1∈R and also 2, 11, 3∈R.
Hence, R is symmetric. But clearly R is not transitive.