Question 6
For any finite set $S,$ let $|S|$ denote the number of elements in $S.$ Find the number of ordered pairs $(A, B)$ such that $A$ and $B$ are (not necessarily distinct) subsets of $\{1, 2, 3, 4, 5\}$ that satisfy $$
|A| \cdot |B| = |A \cap B| \cdot |A \cup B|.
$$
|A| \cdot |B| = |A \cap B| \cdot |A \cup B|.
$$