= Solution
The preceding proofs show that this inclusion forces both <symmetry> and <transitivity> of $T$; its <reflexivity> already follows from that of $R,S$. It actually forces equality of the composites, not just a one-way inclusion:
$$
\boxed{S\circ R\subseteq R\circ S\quad\Longleftrightarrow\quad S\circ R=R\circ S.}
$$
This is the <composition of commuting equivalence relations> criterion. It remains to establish the asserted smallest-extension characterization, rather than merely to identify an <equivalence relation>.
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