1. Given the set $A=\{x \in \mathbf{R}|| x-2 \mid \leqslant 1\}$, set $B=\left\{x \in \mathbf{R} \left\lvert\, \frac{x-5}{2-x}>0\right.\right\}$. Then $A \cap B=$
- 1. $\{x \mid 2<x \leqslant 3\}$.

It is easy to see that $A=\{x \mid 2 \leqslant x \leqslant 3\}, B=\{x \mid 2<x<5\}$.