\(A\subset B\Leftrightarrow\left\{{}\begin{matrix}1>m\\3< m+2\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}1>m\\m>1\end{matrix}\right.\Leftrightarrow m\in\varnothing\\ B\subset A\Leftrightarrow\left\{{}\begin{matrix}m>1\\m+2< 3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}m>1\\m< 1\end{matrix}\right.\Leftrightarrow m\in\varnothing\)