Let R, S are two symmetric relations and SoR, RoS are their composite relations. Then which of the following is true?

Suppose that $R\circ S$ is symmetric

$\begin{array}{rcl}{\left(R\circ S\right)}^{-1}& =& S^{-1}\circ R^{-1}\\ R\circ S& =& S\circ R\end{array}$

It implies that $ROS$ is symmetric only when $\begin{array}{rcl}{\left(R\circ S\right)}^{-1}& =& S\circ R\end{array}$

Similarly $SOR$ is symmetri only when $\begin{array}{rcl}{\left(S\circ R\right)}^{-1}& =& R\circ S\end{array}$