1. Let $A$ and $B$ be two non-empty finite sets, and the universal set $U$
$$
\begin{aligned}
= & A \cup B, \text{ and } |U|=m. \text{ If } \\
& \left|\left(\complement_{U} A\right) \cup\left(\complement_{U} B\right)\right|=n,
\end{aligned}
$$

then $|A \cap B|=$
$$
-1 . m-n \text {. }
$$

Notice that,
$$
\left(\complement_{U} A\right) \cup\left(\complement_{U} B\right)=\complement_{U}(A \cap B) .
$$

From the Venn diagram, we know $|A \cap B|=m-n$.