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Can the mu (10) Rockn Upload Assl mens neck gold crossn Black Starn a. Every person has a friend. b. It is not the case that any student would get a good grade without studying. c. Two persons are siblings if their parents are the same. d. There are happy moments in everyone's life. e. Some people in the community has cats, and some people have dogs. f. Some students play computer games all the time. (bonus problem 1 point). g. It is not the case that a person can be happy and sad at the same time (bonus problem 1 point). 11. Let P (, y) be the statement"Student x has taken class y," where the domain for x consists ofall 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) a. 3x 3y P(x, y). b) 3x Vy P (x, y). e) Vx 3y P (x, y). d) Vx Vy P(x, y statementxyx-y If the domain for both variables consists of all integers, what are the truth values? (2 points each = 10 points) 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 points) a) 3x 3y P(x, y). b) Vr Vy Q(x, y). c) , ay (Q(y) ^ Vx R(x, y). 6 MacBook Air 4 5 8 9 0