Does S has to be transitive?

Question

Let R,S be relations over A when R is a partially ordered set, S is a s symmetrical relation $R \subset S$. Does S has to be transitive?

Thanks in advance!

Answer 1

$A=\{0,1,2\}$, $R=\emptyset$, $S=\{(0,1),(1,0), (1,2), (2,1)\}$ seems to me to be a counterexample.