1. Let $A \cup B=\{1,2, \cdots, 10\},|A|=|B|$. Then the number of all possible ordered pairs of sets $(A, B)$ is
- 1. 9953.

If $|A|=k(k=5,6, \cdots, 10)$, then $A$ has $\mathrm{C}_{10}^{k}$ possibilities.

For each possibility of $A$, since $A \cup B=\{1,2, \cdots, 10\}$, we know that $C_{A \cup B} A \subseteq B$.
Thus, $B$ already has $10-k$ elements.
To ensure $|A|=|B|$, it is necessary to select $2 k-10$ elements from $A$ to belong to $B$, hence, $B$ has $\mathrm{C}_{k}^{2 k-10}$ possibilities. Therefore, the ordered set pair $(A, B)$ has $\mathrm{C}_{10}^{k} \mathrm{C}_{k}^{2 k-10}$ possibilities.

Noting that $k=5,6, \cdots, 10$, the total number of all possible ordered set pairs $(A, B)$ is
$$
\begin{array}{l}
\sum_{k=5}^{10} \mathrm{C}_{10}^{k} \mathrm{C}_{k}^{2 k-10}=\mathrm{C}_{10}^{5} \mathrm{C}_{5}^{0}+\mathrm{C}_{10}^{6} \mathrm{C}_{6}^{2}+\cdots+\mathrm{C}_{10}^{10} \mathrm{C}_{10}^{10} \\
=8953
\end{array}
$$