1. The problem statement, all variables and given/known data Express each of these statements using quantifiers. Then form the negation of the statement so that no negation is to the left of a quantifier. Next, express the negation in simple English. (Do not simply use the phrase “It is not the case that.”) a) Every student in this class has taken exactly two mathematics classes at this school. b)Someone has visited every country in the world except Libya. c) No one has climbed every mountain in the Himalayas. d)Every movie actor has either been in a movie withKevin Bacon or has been in a movie with someone who has been in a movie with Kevin Bacon. 2. Relevant equations 3. The attempt at a solution I just simply wanted to know if I was beginning correctly. For a), would the statement translate into [itex]\forall x \exists ! y \exists ! z ((S(x,y) \wedge S(x,z)) \implies (y \ne z[/itex], where S(x,y) is, " Student x has taken mathematics course y"? For b), would the statement translate into [itex]\exists x \forall y ((V(x,y) \wedge \neg V(x, Lybia))[/itex], or would it be [itex]\exists x \forall y ((V(x,y) \wedge y \ne ~Lybia)[/itex], where V(x,y) is, "x has visited country y."?