Question 1: Resolving Problems

Are the following arguments valid or not? Use resolution or resolution refutation to find out. Proceed in four steps:

Extract the propositions from the argument and name them with single letters.

Describe the hypotheses and the conclusion in propositional calculus.

Convert these expressionsinto conjunctive normal form (CNF)suitable for resolution or resolution refutation (whichever method you decide to use).

List the steps of the resolution (refutation) and state the result, that is, whether the argument is valid or not.

a) Frank and Sarah take the AI course at UMass Boston. Sarah and George take the Discrete Math course at UMass Boston. Whoever takes the AI course at UMass Boston ends up in a lunatic asylum. Whoever takes the Discrete Math course at UMass Boston loses all their hair. Therefore, Sarah will lose all her hair and end up in a lunatic asylum.

b) Anne goes to the library on Saturday or on Sunday. John also goes to the library on Saturday or Sunday. Therefore, both Anne and John will be at the library on Saturday, or both of them will be at the library on Sunday.

c) If we could travel backwards in time, we could visit ourselves in the past. If we could visit ourselves in the past, someone would have done so. If someone had visited him/herself in the past, the visited person would publicize that event. No such event has ever been publicized. Therefore, we cannot travel backwards in time.

d) Whenever Carl drinks a bottle of whiskey, he gets terrible headaches. Whenever Carl drinks a bottle of rum, he believes he sees pink elephants. Whenever Carl drinks a bottle of water, he feels bored. He drinks one or more bottles, each of them containing whiskey, rum, or water. Carl does not believe he sees pink elephants, and he is not bored. Therefore, he must have drunk a bottle of whiskey.

e) Jennifer is either watching a soccer game or a baseball game, or both. Whenever she watches a soccer game, she wears a Beckham t-shirt. Whenever she watches a baseball game, she wears a Red Sox scarf. Therefore, Jennifer is wearing a Beckham t-shirt and a Red Sox scarf.