Homework Help is Here – Start Your Trial Now!
Math
Calculus
Fill in the blanks. Let R(X) = "x owns a red convertible", S(x) = "x has gotten at least one speeding ticket", and C(x) = "x is a student in our class" , where the domain of x consists of all people in the world. Premises in logical form, therefore, will be C(linda), C(Linda) ^ R(Linda) and Vx(R(x)→ S(x)). (1) Vx(R(x) → S(x)) (2) R(Linda) → S(Linda) instantiation from (1) (3) C(Linda) ^ R(Linda) Premise (4) C(Linda) from (3) (5) R(Linda) from (3) (6) S(Linda) Modus ponens from and (5) (7) C(Linda) A S(Linda) from (4) and (6) (8) 3x(C(x) ^ S(X)) Existential from Step (8) expressed in words is "Therefore, someone in the class has gotten at least one speeding tícket".

Fill in the blanks. Let R(X) = "x owns a red convertible", S(x) = "x has gotten at least one speeding ticket", and C(x) = "x is a student in our class" , where the domain of x consists of all people in the world. Premises in logical form, therefore, will be C(linda), C(Linda) ^ R(Linda) and Vx(R(x)→ S(x)). (1) Vx(R(x) → S(x)) (2) R(Linda) → S(Linda) instantiation from (1) (3) C(Linda) ^ R(Linda) Premise (4) C(Linda) from (3) (5) R(Linda) from (3) (6) S(Linda) Modus ponens from and (5) (7) C(Linda) A S(Linda) from (4) and (6) (8) 3x(C(x) ^ S(X)) Existential from Step (8) expressed in words is "Therefore, someone in the class has gotten at least one speeding tícket".

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
The steps below demonstrate how the premises "Linda, a student in this class, owns a red convertible" and "Everyone who owns a red convertible has gotten at least one speeding ticket" lead to the conclusion "Someone in this class has gotten a speeding ticket." Fill in the blanks. Let \( R(x) \) = "x owns a red convertible", \( S(x) \) = "x has gotten at least one speeding ticket", and \( C(x) \) = "x is a student in our class", where the domain of x consists of all people in the world. Premises in logical form, therefore, will be \( C(Linda), \; C(Linda) \land R(Linda) \) and \( \forall x (R(x) \rightarrow S(x)) \). 1. \(\forall x(R(x) \rightarrow S(x))\) 2. \( R(Linda) \rightarrow S(Linda) \) instantiation from (1) 3. \( C(Linda) \land R(Linda) \) Premise 4. \( C(Linda) \) from (3) 5. \( R(Linda) \) from (3) 6. \( S(Linda) \) Modus ponens from (2) and (5) 7. \( C(Linda) \land S(Linda) \) from (4) and (6) 8. \( \exists x(C(x) \land S(x)) \) Existential from (7) Step (8) expressed in words is "Therefore, someone in the class has gotten at least one speeding ticket."
Transcribed Image Text:The steps below demonstrate how the premises "Linda, a student in this class, owns a red convertible" and "Everyone who owns a red convertible has gotten at least one speeding ticket" lead to the conclusion "Someone in this class has gotten a speeding ticket." Fill in the blanks. Let \( R(x) \) = "x owns a red convertible", \( S(x) \) = "x has gotten at least one speeding ticket", and \( C(x) \) = "x is a student in our class", where the domain of x consists of all people in the world. Premises in logical form, therefore, will be \( C(Linda), \; C(Linda) \land R(Linda) \) and \( \forall x (R(x) \rightarrow S(x)) \). 1. \(\forall x(R(x) \rightarrow S(x))\) 2. \( R(Linda) \rightarrow S(Linda) \) instantiation from (1) 3. \( C(Linda) \land R(Linda) \) Premise 4. \( C(Linda) \) from (3) 5. \( R(Linda) \) from (3) 6. \( S(Linda) \) Modus ponens from (2) and (5) 7. \( C(Linda) \land S(Linda) \) from (4) and (6) 8. \( \exists x(C(x) \land S(x)) \) Existential from (7) Step (8) expressed in words is "Therefore, someone in the class has gotten at least one speeding ticket."
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS