Only solve Q11(d,e,f) & Q14(q,c), Q30(a,c) please

11. Let S(x) be the predicate "x is a student," F(x) the pred- icate "x is a faculty member," and A(X, y) the predicate "x has asked v 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 by a 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 d) All students in this class have learned at least one pro- gramming language. e) There is a student in this class who has taken ev- ery course offered by one of the departments in this f) Some student in this class grew up in the same town g) Every student in this class has chatted with at least 15. Use quantifiers and predicates with more than one vari- a) Every computer science student needs a course in dis- school. as exactly one other student in this class. one other student in at least one chat group. able to express these statements. crete mathematics. 30. Rewrite each of these statements so that negations ap- pear only within predicates (that is, so that no negation is outside a quantifier or an expression involving logical connectives). a) -3y3x P(x, y) e) -3y(V3zT(x, y, z) v 3xVzU(x, y, z))