Problem 2. Express the following statements in logic using predicates and quantifiers. Then negate each statement and reformulate it using only , A, and V as operators, so that no negation symbol precedes a quantifier. Simplify the obtained statements and then express them again in the English language. (a) \"Every student who passes the exam, passes the course.\" . [3 points] (b) \"There is a person who has eaten at every restaurant in Regina, but not at any restaurants outside Regina.\" [4 points| Problem 3. Suppose Vz ((z) V Q(zx)) is true. Does that imply that also V (P(z)) Vv Vz (Q(z)) is true? Prove your claim. . [3 points] Problem 4. Formulate the following English language statements in propositional logic and write them in form of an inference rule. Which inference rule from class is used in this inferenee? \"If T work hard, I can do the assignments.\" \"If T can do the assignments, T will pass the exam.\" \"Therefore, if T work hard, T will pass the exam.\" . ' [3 points]