Is it me or is this question wrong?
I keep books, I have 40 books. 11 are comedy, 20 are horror, and 18 are fiction. 3 are horror and comedy, 6 are horror and fiction, and 2 are comedy and fiction. How many are fiction and comedy, but not horror?
Wouldn't the answer just be 2? If not could someone explain?
If $C$ is the set of comedy books, $H$ the set of horror books, and $F$ the set of fiction books, then
$$|C\cup H\cup F|=|C|+|H|+|F|-\left(|C\cap H|+|H\cap F|+|C\cap F|\right)+|C\cap H\cap F|$$
by the inclusion-exclusion principle, so
$$40=11+20+18-(3+6+2)+|C\cap H\cap F|\;,$$
and $|C\cap H\cap F|=40-49+11=2$. That is, there are $2$ books that are in all three categories. This means that both of the books that are comedy and fiction must also be horror, so there are no books that are fiction and comedy but not horror.