Problem 3 [35pts] a) [20pts| Express each of the following statements using quantifiers and logical operators. Then, form the negation of the statement so that no negation is to the left of a quantifier. In doing so, correctly specify your universe of discourse. [4pts] All dogs have fleas. * [4pts] There is a horse that can add [4pts] Every koala can climb [4pts] No monkey can speak French . [4pts] There exists a pig that can swim and catch fish. b) [10pts] Show that yx(P(x) Q(x))-yxP(x) yo(x). Show all your work. c) [5pts] Let Q(x.y) be the statement "x + y > 0". If the domain for both variables consists of all integers, what are the truth values for the following propositions: * [lpt] 3x3yQ(x, y) [lpt] Vx3yQ(x,y)