$A\cap B=\emptyset$ thì
$\left[ \begin{array}{l} 2m+1\le2 \\ 2m-1\ge3\end{array} \right .\Leftrightarrow\left\{ \begin{array}{l} m\le\dfrac{1}{2} \\m\ge2\end{array} \right .$
$A\cap B\ne\emptyset$ thì
$\left[ \begin{array}{l} 2m-1\le2<2m+1\\ 2m-1<3\le2m+1\end{array} \right .\Leftrightarrow \left[ \begin{array}{l} \dfrac{1}{2}<m\le\dfrac{3}{2}\\ 1\le m<2\end{array} \right .$ $\Leftrightarrow \dfrac{1}{2}< m< 2$
$A\subset B$ thì
$\left\{ \begin{array}{l} 2<2m-1 \\ 2m+1<3\end{array} \right .\Leftrightarrow \left\{ \begin{array}{l} m>\dfrac{3}{2} \\ m<1\end{array} \right .$(vô nghiệm)
$B\subset A$ thì
$\left\{ \begin{array}{l} 2m-1\le2\\ 3\le2m+1\end{array} \right .\Leftrightarrow \left\{ \begin{array}{l} m\le\dfrac{3}{2} \\ m\ge1\end{array} \right .$ $\Leftrightarrow 1\le m\le \dfrac{3}{2}$
$A\cup B=()$ thì
$\left\{ \begin{array}{l} 2<2m-1 \\3>2m+1 \end{array} \right .\Leftrightarrow \left\{ \begin{array}{l} m>\dfrac{3}{2} \\ m<1\end{array} \right .$ (loại)
$A\cup B=[]$ thì
$\left\{ \begin{array}{l} 2\ge2m-1 \\3\le2m+1 \end{array} \right .\Leftrightarrow1\le m\le\dfrac{3}{2}$
