Discrete Mathmatics

4. 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. c) Vx3yP(x, y) e) Vyax P(x, y) 11. Let S(x) be the predicate "x is a student," F(x) the pred- icate "r is a faculty member," and A (x, y) the predicate has asked y a question," where the domain consists of all people associated with your school. Use quantifiers to express each of these statements a) Lois has asked Professor Michaels a question. b) Every student has asked Professor Gross a question. c) Every faculty member has either asked Professor Miller a question or been asked a question by Pro- d) Some student has not asked any faculty member a e) There is a faculty member who has never been asked f) Some student has asked every faculty member a ques- g) There is a faculty member who has asked every other h) Some student has never been asked a question bya fessor Miller question. a question by a student. tion. faculty member a question faculty member 14. Use quantifiers and predicates with more than one vari- able to express these statements. a) There is a student in this class who can speak Hindi. b) Every student in this class plays some sport. c) Some student in this class has visited Alaska but has not visited Hawai. gramming language ery course offered by one of the departments in this d) All students in this class have learned at least one pro- e) There is a student in this class who has taken ev- school. as exactly one other student in this class. one other student in at least one chat group. f) Some student in this class grew up in the same town g) Every student in this class has chatted with at least