CS 4804 Homework #4

1. (50 points) Represent the following sentences in first-order logic, using a consistent vocabulary (which you must define):
   
   
   • Not all students take both CS 4804 and CS 5804.
   • Only one student failed in HIST 4804.
   • Only one student failed in both HIST 4804 and BIOL 4804.
   • The best score in HIST 4804 was better than the best score in BIOL 4804.
   • You can only fail a course if you take it.
   
   
2. (50 points) You are given the following facts:
   
   
   This is a tale of three professors - Dr. Flexy, Dr. Accommodating, and Dr. Strict. Dr. Flexy is willing to teach CS 4604 as well as CS 4104. Dr. Accommodating is willing to teach CS 4604 as well as CS 4804. Dr. Strict would like to teach only CS 4104. All three courses - CS 4104, CS 4604, and CS 4804 - must definitely be taught. Each professor can teach only one course at a time.
   
   State these facts (and any more that you need) in predicate logic (in a suitably defined vocabulary, which you must state), and use resolution-refutation to determine who should teach each course. For full credit, clearly state the vocabulary, describe how the given facts are encoded, convert them to clauses, and prove a contradiction.