Complete the logical proof for the following argument.ExP(x)Vx(P(x) → Q(x))StepPropositionJustificationExP(x)Hypothesis2 c is an element in the domain AP(c) essential specificationc is an element in the domainessential specificationvx(P(x)¬Q(x))Hypothesis5P(c) → Q(c)Universal Specification,6P(c)Simplification, 27Q(c)ExQ(x)Conclusion4.

We will go through the logical proof table given above. We will be using the following statements.…

Answered: Complete the logical proof for the…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterA: Appendix

SectionA.1: Algebraic Expressions

Problem 2E

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Suppose P(x) is some predicate for which the statement ∀xP(x) is true. Is it also the case that ∃xP(x) is true? In other words, is the statement ∀xP(x) → ∃xP(x) always true? Is the converse always true? Assume the domain of discourse is non-empty. Explain.
Let P(x) = "x studies Calculus", Q(x) = "x is a Computer Science major", R(x) = "x knows JavaSckript" Match given quantified statements with their logical form. Every Computer Science major studies Calculus A. Domain = set of all Computer Science majors 3xR (x) Some Computer Science majors study Calculus B. Domain = set of all students v Every Computer Science major knows JavaScript 3x (Q (x) λP (x) ) C. Domain = set of all Computer Science majors There is a Computer Science major who can program on JavaScript VxP (x) D. Domain = set of all people Vx (Q (x) R (x)
Which of the following are Predicates? P1(x): 16x+5 P2(x): x is even P3(x): 16 is odd P4(x,y): x+y=10 P5(x): Program x terminates
Let P (x) be the statement “ x2 > 1 ” and Q(x) be the statement “x+1 < 4”.The universe of discourse consists of all real numbers. What are the truthvalues for the following:i. ∀x(P (x) →Q(x))ii. ∃x(P (x) →Q(x))iii. ∀x(P (x) ∧Q(x))iv. ∃x(P (x) ∧¬Q(x))
Let p(x) be the statement “x can speak Arabic” and let Q(x) be the statement “x knows the computer science language Java.” Express each of these sentences in terms of p(x), q(x), quantifiers and logical connectives. The domain for quantifiers consists of all students at your school. There is a student at your school who can speak Arabic and who known Java. There is a student at your school who can speak Arabic but who doesn’t know Java. Every student at your school either can speak Arabic or knows Java. No student at your school can speak Arabic or knows Java.
let P and Q be predicates on some domain of discourse D and define p = Vx (P(x)) → Vx (Q(x)) q = Vx ( P(x) → Q(x) ). Check all statements that must be true. O If q is true, then p is true. None of the other choices. If p is true, then q is true.
Let Q(x, y) be the statement "student x has been a contestant on quiz show y." Express "At least two students from your school have been contestants on Jeopardy." in terms of Q(x, y), quantifiers, and logical connectives, where the domain for x consists of all students at your school and for y consists of all quiz shows on television. A ax13x2(Q(x1, Jeopardy) ^ Q(x2, Jeopardy) A x1 = x2) B) vyaxQ(x, Jeopardy) c) ax(Q(x, Jeopardy) ^ Q(x, y)) D none of the choices
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With the attached image what would the translation in english be? Would it be something like: There exists a sports car for all expensive cars that is not safer?
The domain for this problem is some unspecified collection of numbers. Consider the predicate P(x, y) = "x is greater than y." (a) Translate the following statement into predicate logic. Every number has a number that is greater than it. (x)(3)(x, y) (x), x) (3x)(y), x) (x)(³)(y,x) Ⓒ (3x)(³y)P(y,x) (b) Negate your expression from part (a), and simplify it so that no quantifier or connective lies within the scope of a negation. O (3x)(3)(~P(y, x)) ((((, x)) (3x)(V)(P(x, y)) (3x)(V)(Py, x)) (x)(3)(Py, x)) (c) Translate your expression from part (b) into understandable English. Don't use variables in your English translatio O All numbers have a number that they are less than or equal to. O There is a number that has a number that it is less than or equal to. O There is a number that all numbers are greater than or equal to. O There is a number that all numbers are less than or equal to. O All numbers are less than or equal to all numbers.
1) Let I(x) be the statement “x has an Internet connection” and C(x, y) be the statement “x and y have chatted over the Internet,” where the domain for the variables x and y consists of all students in your class. Use quantifiers to express each of these statements. Jerry has an Internet Rachel has chatted over the Internet with Jan and Sharon have never chatted over the Everyone in the class has chatted with Sanjay has not chatted with everyone except Someone in your class does not have an Internet Not everyone in your class has an Internet Exactly one student in your class has an Internet Everyone except one student in your class has an Internet Everyone in your class with an Internet connection has chatted over the Internet with at least one other student in your Someone in your class has an Internet connection but has not chatted with anyone else in your There are two students in your class who have not chatted with each other over the There is a student in your class who has…
Proficiency #8. Which of the following are logically equivalent to the statement -[(Vx E U) (¬p(x) V q(x))] if U is the set of all parrots, p(x) is the statement "x is talkative", q(x) is the statement “x is green" (Choose all that apply): I. There is an parrot who is not green and is talkative. II. No talkative parrots are green. III. All green parrots are talkative. IV. Not all parrots are not green. V. At least one talkative parrot is not green. VI. Not all talkative parrots are green.

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