CS 4804 Homework #3

1. (9 points) Problem 7.5 of your textbook (all three parts).
   
   
2. (32 points) Problem 7.8 of your textbook (all parts). Even though the question suggests that you can use truth tables, you should solve these problems using the equivalence rules of Fig. 7.11.
   
   
3. (9 points) Problem 8.7 of your textbook (note the presence of the word "languages" in "All Germans speak the same languages").
   
   
4. (20 points) Problem 8.9 of your textbook.
   
   
5. (10 points) Problem 8.13 of your textbook.
   
   
6. (20 points) You are given the following paragraph: "Tony, Mike, and John belong to the Alpine Club. Every member of the Alpine Club is either a skier or a mountain climber or both. No mountain climber likes rain, and all skiers like snow. Mike dislikes whatever Tony likes and likes whatever Tony dislikes. Tony likes rain and snow."
   
   Represent the above information in first order predicate logic sentences in such a way that you can represent the question "Who is a member of the Alpine Club who is a mountain climber but not a skier?" as a predicate logic expression. Pick a suitable resolution refutation first-order inference rule (e.g., forward chaining, backward chaining, resolution refutation) and use it to answer this question.