1. Let $m, n \in \mathbf{N}^{*}$, and $m>n$, sets $A=\{1,2, \cdots, m\}, B=\{1,2, \cdots, n\}$. If $C \subseteq A$, then the number of sets $C$ that satisfy $B \cap C \neq \varnothing$ is $\qquad$
1. $2^{m-n}\left(2^{n}-1\right)$.

Since the subsets of $A$ that consist only of positive integers $n+1, n+2, \cdots, m$ taken in any combination are the only ones that can satisfy $B \cap C=\varnothing$, and there are $2^{m-n}$ such sets. Therefore, the number of $C$ that satisfy $B \cap C \neq \varnothing$ is $2^{m}-2^{m-n}=2^{m-n}\left(2^{n}-1\right)$.