If A and B are two different nonempty sets, how many distinct sets can be formed with these sets using as many unions,intersections,complements and parentheses as desired.
Four sets are fundamental:$A$,$B$,$A \cup B$,$A \cap B$.
Other sets are A \cup B',$A' \cup B$,$A \cap B'$,$A' \cap B$,$A' \cup B'$,$A' \cap B'$. Any other sets are possible.