 
Summary: G52PAS 20112012 Answers to the exercise on SAT
1. Express the following problem in propositional logic:
I want to invite some of the following people to a party: Alice,
Ben, Chris and Dave. If I invite Alice, I would also have to
invite Ben. I cannot invite Ben and Chris to the same party.
I want to invite at least three of them (this condition you also
need to express as a logical formula).
Answer. Let A stand for inviting Alice and so on.
S1 A B (if invite Alice, then also invite Ben)
S2 ¬(B C) (cannot invite Ben and Chris at the same time)
At least three of them: we can write this as
(A B C) (A B D) (A C D) (B C D)
which is more natural.
However, it is also possible to say that we do not any two of them to be
uninvited: S3
¬(¬A¬B)¬(¬A¬C)¬(¬A¬D)¬(¬B¬C)¬(¬B¬D)¬(¬C¬D)
2. Rewrite the formulas above in CNF (hint: the last condition, about invit
ing at least three people, is a bit of a pain to rewrite to CNF if you
express it in the obvious way to begin with. It may be easier to work with
an equivalent condition, `I do not want to exclude any two of them from
