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 y a question," where the domain consists ofall people associated with your school. Use quantifiers toexpress 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 ProfessorMiller a question or been asked a question by Pro-fessor Miller.d) Some student has not asked any faculty member aquestion.e) There is a faculty member who has never been askeda question by a student.f) Some student has asked every faculty member a ques-tion.g) There is a faculty member who has asked every otherfaculty member a question.h) Some student has never been asked a question by afaculty member.

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Answered: 11. Let S(x) be the predicate "x is a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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5. Rewrite the following proposition as unambiguous English sentences. The relevant predicates are defined as follows: Again, let’s let P be a set of all people a. A(x) means “x is teaching the AI course" b. T(x) means “x is taking AI course" c. F(x) means “x has a twitter account." d. C(x) means “x likes to read." For example, the proposition 3x {P[A(x)^ C(x)]} could be translated as "There is a person who is teaching and likes to read" P [T(x) → (F(x) C(x))] ?
Question 6 Plz send hand written answer asap
a 1. Consider the open sentence P(a, b) : > 1., where the domain of a is A = {-4,3,5} and the b domain of b is B = {-3,2,4}. a a) State the quantified statement R: Va € A, 3b € B, > 1. in words. b b) State -R in symbols. c) State - R in words. d) Determine, with justification, whether R is true.
1-Translate the statements using quantifiers: 1-No English majors like taking Chemistry classes 2-There is a student who is majoring in Aviation but has a roommate majoring in Literature. Sx: is a student Ax: majoring in Aviation R(x,y):y is roommate of x Lx: majoring in literature 3- every student in your class has contacted another student in your class by email or text who replied using the same method of communicating
Express this in predicate logic: Each email address has exactly one email box. M(x): x is an email address B(x,y): x has an email box y
Given the domains m e MOVIES and ce CHARACTERS and the following predicates: • sW(m): m is a Star Wars movie. A(c, m): c is a character who appears in the movie m • D(c): c is a Droid. • L(m): I liked m. • Q(c, q): c says q (e is quoted as saying q.) • jarjar is the character Jar Jar Binks • bad is the quote: "I've got a bad feeling about this!"
8. Use quantifiers and predicates with more than one variable to express this statement: “There a person in your class who has taken every math class at Liberty University." Let the domain of x be all people and the domain of y be all classes.
Exercise 1. Express the following statements symbolically using multiple quantifiers. De- fine your domains and two-variable predicates. Then negate the statements. (a) Every rational number when multiplied by some integer is an integer. Domain(s): • Predicate: • Statement: • Negation: ● Englsih translation of negation: . Which is true? The original statement or its negation? Justify your answer.
Write these statements formally using quantifiers and predicates. Domain is days of the year. S(x): x is sunny R(x): x is rainy a. Every day is sunny b. Some days are rainy c. There are some days that are rainy and sunny d. There are some days that, if they are sunny, then they are not rainy
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