Using the elements of sets $A$ and $B$, each with 9 elements and consisting of letters,
- soldier,
- painter,
- academic
two of these words can be written with the elements of the $A \cap B$ set, and the other can be written with the elements of the $A \cup B$ set.
Accordingly, which of the following cannot definitely be written with the letters in set $A$?
A) poet
B) doctor
C) clerk
D) artist
E) secretary