Let P(x) be the statement "x spends more than five hours every weekday in class"" wherethe domain for x consists of all students. Express the quantification 3x -P(x) in English.A. No student spends more than five hours every weekday in class.OB. Every student spends more than five hours every weekday in class.OC. There is a student who does not spend more than five hours every weekday in class.O D. There is a student who spends more than five hours every weekday in class.QUESTION 6Which of the following statements is true?OA. (0} e {0}B. øe {0}Oc (e) < (0}OD. (0} c {0}QUESTION 7Translate these statement vx(C(x) - F(x)) into English, where C(x) is "x is a comedian"and F(x) is "x is funny" and the domain consists of all people.O A. Every funny person is a comedian.OB. There exists a funny comedian.OC. Every person is a funny comedian.OD. Every comedian is funny.QUESTI ON 8

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Answered: Let P(x) be the statement "x spends…

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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2 Translating English Sentences into Formulas Consider the following two predicates: S(x) : x is a student in CSE015; M(x) : x plays a musical instrument. Let the domain be the set of all people. Using the above predicates, translate the following sentences into formulas using the appropriate quantifiers and operators. a) Not every student in CSE015 plays a musical instrument. b) A person is either a student in CSE015 or plays a musical instrument, but not both. c) There exists at least one student in CSE015 who does not play a musical instrument.
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
Tarski World a g. Using the following predicates: square (x) is true if x is a square (otherwise it is false) star(x) is true if x is a star (otherwise it is false) circ(x) is true if x is a circle (otherwise it is false) shade (x) is true if x is shaded (otherwise it is false) next.to(x, y) is true if x and y are adjacent horizontally, vertically or diagonally. This relation is not reflexive for any object. For each of the statements below, determine whether the statement is true or false. You need not justify your response. 3xcirc(x) A shade(xr) Va shade(r) V ¬shade(r) Va square(r) → ¬shade(r) Vævy(star(r) A ¬shade(r) A next.to(x, y) → shade(y) ^ circ(y)) vr next.to(x, y) A shade(r) 3rvy next.to(r, y) A shade(r)
For each quantified expression below the universe of discourse is U = {1,2,3}. Carefully negate each expression and state whether the original statement or your negation is true. a. 3x such that Vy,x² < y + 1. b. Vx, 3y such that x² + y² < 12. c. Vx Vy,x2 + y² < 12.
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
Let M(x,y) be the predicate "person x has seen movie y," where the domain for x is the set of all people and the domain for y is the set of all movies. Express the following English sentence as a symbolic proposition: "There is a movie that has not been seen by any people." x-M(x,y) ⒸyVx-M(x, y) x-M(x,y) yx M(x,y) -
Use a quantifier to make the following true or false, as indicated, where x is a natural number. x + x =12 (make true)
. If the domain consists of all animals, express the following statements in terms of quantifiers and logical connectives, where B ( x ) = x is a bear, G ( x ) = x raids garbage cans, H ( x ) = x loves honey, and T ( x ) = lives in tents. A bear lives in a tent. Bears love honey. Only bears raid garbage cans. No bear lives in a tent. Some bears do not love honey.
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.
Paraphrase the following into quantificational notation: (a) If any student taking Logic cheats, then every student taking Logic will be unhappy. (b) If any student taking Logic cheats, then he or she will be unhappy. (c) Logic students are either clever or happy. (d) If anything is both gaseous and liquid, then it is a plasma. (e) No plasma is a liquid unless some plasma is a gas.
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.
Discrete Math. This question is based on predicates and quantifiers. Please show all work and identify the type of each given statement to its correct match.

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