II. Define the predicate r(x) with the universe of discourse R byr(x) : ((Ve < 0) x > c) →x = 0.1. Find the truth values of the following.(a) r(-1)(b) r(0)(c) r(1)2. Write ~r(x) such that there should be no negation before quantifiers nor before a logicalconnective.

The predicate rx with the universe of discourse ℝ defined as follows: rx : ∀c<0 x≥c→x=0 1. a)…

Answered: II. Define the predicate r(x) with 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.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 10CT: Statement P and Q are true while R is a false statement. Classify as true or false:...

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Statement P and Q are true while R is a false statement. Classify as true or false: a)PorQb)(PandQ)orR
4. Suppose that the variable x represents people, and F(x): "x is friendly" T(x): "x is tall" A(x): "x is angry". Express each of the following statements using these predicates, quantifiers, and logical connectives. (a) Some people are not angry. (b) All tall people are friendly. (c) No friendly people are angry.
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.
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…
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))
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 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))
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.
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))
(d) 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 truth values for the following: i. Væ(P(x) → Q(x)) ii. Jx(P(x) → Q(x)) iii. Vr(P(x) A Q(x)) iv. 3x(P(x) A -Q(x))
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)
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II. Define the predicate r(x) with the universe of discourse R by r(x) : ((Ve < 0) x 2 c) →x = 0. 1. Find the truth values of the following. (a) r(-1) (b) r(0) (c) r(1) 2. Write ~ r(x) such that there should be no negation before quantifiers nor before a logical connective.