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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Let T(x) be the predicate "person x is a teacher" and V(x) be the predicate "person x plays video games." Express the following English sentence as a symbolic proposition: "All teachers play video games." 3x(T(x) ⇒ V(x)) ³x(T(x) ^ V(x)) OVx(T(x) ^ V(x)) Ⓒ\x(T(x) ⇒ V(x))
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.
Discrete mathematics
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)
Write a logical proof to prove that the following argument is valid. Wx(P(x) — Q(х)) Ex(R(x) ^ P(x)) -: Ex(R(x) ^ Q(x)) Hint: To plug in the same value to instantiate both existential quantifiers and universal quantifiers, instantiate the existential quantifier before the universal quantifier. There are two ways to submit answers to this question: 1) Eneter in essay box directly. Note that logical expressions must be entered in Math mode, which begins with \(, and end with \). Below is a list of LaTex code for each logical operator. V \vee A \wedge - \neg → \to + \leftrightarrow Vx \forall x Ex \exists x For example, to enter Vx(P(x) ^ Q(x)), \(\forall x (P(x) \wedge Q(x)) \). You can check the format of your answer by clicking "Preview My Answers".
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.
In the following argument, give a justification for each step.
Let B(x) be the predicate "person x is a fan of the Bulldogs" and let y(x) be the predicate "person x is a fan of the Yellow Jackets," where the domain for the variable x is the set of all people. Express the following symbolic proposition as an English sentence: 3x(B(x) VY(x)) Some person is a fan of the Bulldogs or a fan of the Yellow Jackets. Every person is a fan of the Bulldogs or a fan of the Yellow Jackets. Some person is a fan of the Bulldogs and a fan of the Yellow Jackets. Every person is a fan of the Bulldogs and a fan of the Yellow Jackets.
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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