G52PAS 2011-2012 Answers to the exercise on SAT 1. Express the following problem in propositional logic Summary: G52PAS 2011-2012 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 Collections: Computer Technologies and Information Sciences