11. Let P (x, y) be the statement "Student x has taken class y," where the domain for x consists of all students in your class and for y consists of all computer science courses at your school. Express each of these quantifications in English. (1 points each -4 points) . 3x3xP(x, y). b) 3xVyP(x, y). c)yx3y P (x, y). d)yxyy P(x, y) 12. Let Q(x, y) be the statement "x +y-x- y." If the domain for both variables consists of all integers, what are the truth values? (2 points each-10 points) a. Q(1,1) b) Q(0, 0). c) "y Q(L.y)d) Vx Vy Q(x, y) e) Vx 3y Q(x, y) 13. Rewrite each of these statements so that negations appear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives). (2 points each-6 points)