Transitivity of a composition of partial orders

Question

There's a pair $(X, R)$, $(X, S)$ of partial orders on $X$. There is a linear order $(X, L)$ that is a linear extension for both $R$ and $S$.

I cannot find the right counterexample to show that $R \circ S$ is not transitive. Can anybody help?

Answer 1

From the linear order axbyc,
pick aRx, bRy, xSb, ySc.
Thus aRSb, bRSc but not aRSc.