1. 15 points) Consider a vocabulary with only four propositions A, B, C, and D. Question 1 and 2 are related to the following sentence (we call it Answer the following ls ? satisfiable? C. ls ? unsatisfiable? NO will not give you a point. a. b. Is ? valid? Verify your decisions using truth tables or the equivalence rules. Simply answering YES or 2, (10 points) Convert ? (Question 1) to CNF. Show your step 3. (25 points) Write down a logical representation for the following sentences as a knowledge base. Let us denote this knowledge base with KBS a. Charlie is a student b. Son is a professor c. Al and OOP are the only two available classes. d. Son teaches A e. Some professor teaches OOP f. Each student must take at least one class g. Every class has at least one student and must be taught by at least one professor Use the following predicates in writing the sentences .student(X) (ors(X), for short): X is a student. . professor(X) (or p(X)): X is a professor . class(X) (oc(X)X is a class .teaches(X,Y) (or t(X,Y)): X teaches the class Y . registers(X,Y) (or r(X,Y)): X takes the class Y . eq(X,Y) (or X-Y): X equalsY Prove that Charlie takes Al or OOP using resolution. Show the steps