We suppose to figure out how to represent knowledge and reasoning and any help on the written part of the assignment would be great!

Part I: Written Problems (100 points) 1. Representing Sentences in First-Order Logic (28 points) Suppose the variable r represents students, y represents courses, and A(y): y is an advanced course S(r): r is a sophomore F(x): r is a freshmarn T(x,y): is taking y P(x,y): passed y Write the following statements using these predicates and any needed quantifiers (a) There is a course that every freshman is taking. (b) No freshman is a sophomore. (c) Some freshman is taking an advanced course. d) No one is taking every advanced course. (e) Every freshman passed calculus. (f) No freshman or sophomore takes an advanced course 2. Validity and Satisfiability (8 points) For each of the sentences below, decide whether it is valid, satisfiable, or neither. Verify your decisions using truth tables or the Boolean equivalence rules. (a) (Smoke Fire)SmokeFir) (b) ((Smoke ^ Heat)-+ Fire) ((Smoke-+ Fire) V (Heat-+ Fire)) 3. Models (9 points) Consider a world in which there are only four proposition, A, B, C, and D. How many models are there for the following sentences? Justify your