1. If the set $M=\left\{x \left\lvert\, \log _{\frac{1}{2}}(x-1)>-1\right.\right\}$, $N=\left\{x \mid 1<2^{x}<4\right\}$, then $M \cap N=(\quad)$.
(A) $\{x \mid 1<x<3\}$
(B) $\{x \mid 1<x<2\}$
(C) $\{x \mid 0<x<3\}$
(D) $\{x \mid 0<x<2\}$
-.1. B.
Notice
$$
\begin{array}{l}
x \in M \Leftrightarrow \log _{\frac{1}{2}}(x-1)>-1 \\
\Leftrightarrow\left\{\begin{array}{l}
x-1>0, \\
x-1<\left(\frac{1}{2}\right)^{-1}=2
\end{array} \Leftrightarrow 1<x<3 ;\right.
\end{array}
$$
$$
x \in N \Leftrightarrow 1<2^{x}<4 \Leftrightarrow 0<x<2 \text {. }
$$

Therefore, $M \cap N=\{x \mid 1<x<2\}$.