12. Let the set $I=\{1,2, \cdots, 8\}$. If the non-empty subsets $A$ and $B$ of $I$ satisfy $A \cap B=\varnothing$, then the ordered pair of sets $(A, B)$ is called an "isolated set pair" of $I$. Then, the number of isolated set pairs of the set $I$ is $\qquad$ (answer with a specific number).
12.6050.

Let $A$ be a $k(1 \leqslant k \leqslant 7)$-element subset of $I$. Then $B$ is a non-empty subset of the complement of $I$.
Thus, the number of isolated set pairs is
$$
\begin{array}{l}
\sum_{k=1}^{7} \mathrm{C}_{8}^{k}\left(2^{8-k}-1\right)=\sum_{k=1}^{7} \mathrm{C}_{8}^{k} 2^{8-k}-\sum_{k=1}^{7} \mathrm{C}_{8}^{k} \\
=(1+2)^{8}-\left(\mathrm{C}_{8}^{0} 2^{8}+\mathrm{C}_{8}^{8} 2^{0}\right)-\left(2^{8}-\mathrm{C}_{8}^{0}-\mathrm{C}_{8}^{8}\right) \\
=3^{8}-2^{9}+1=6050
\end{array}
$$