Question 1
Let $F$ be the set of all $n$-tuples $(A_{1}, A_{2}, \ldots, A_{n})$ where each $A_{i}$, $i=1,2, \ldots, n$ is a subset of $\{1,2, \ldots, 1998\}$. Let $|A|$ denote the number of elements of the set $A$. Find the number
$$
\sum_{(A_{1}, A_{2}, \ldots, A_{n})} |A_{1} \cup A_{2} \cup \ldots \cup A_{n}|.
$$
$$
\sum_{(A_{1}, A_{2}, \ldots, A_{n})} |A_{1} \cup A_{2} \cup \ldots \cup A_{n}|.
$$