1. Decide whether each of the following sentences is valid, satisfiable or unsatisfiable: a) Smoke Fire b) SmokeSmoke c) Smoke v Fire v-Fire d) (Smoke Fire) → (Smoke →→Fire) 2. Given the following sentences in propositional calculus: 1. (ru) If it rains, Joe brings his umbrella 2. (uw) If Joe has an umbrella, he doesn't get wet If it doesn't rain, Joe doesn't get wet 3. (rw) Use resolution refutation to prove →w. Joe doesn't get wet 3. Represent the following sentences in first-order logic, using a consistent vocabulary that you define: a) Some students took AI in Spring 2022. b) Every student who takes AI passes it. c) Only one student took AI in Spring 2022. d) No one took AI in Fall 2021.
1. Decide whether each of the following sentences is valid, satisfiable or unsatisfiable: a) Smoke Fire b) SmokeSmoke c) Smoke v Fire v-Fire d) (Smoke Fire) → (Smoke →→Fire) 2. Given the following sentences in propositional calculus: 1. (ru) If it rains, Joe brings his umbrella 2. (uw) If Joe has an umbrella, he doesn't get wet If it doesn't rain, Joe doesn't get wet 3. (rw) Use resolution refutation to prove →w. Joe doesn't get wet 3. Represent the following sentences in first-order logic, using a consistent vocabulary that you define: a) Some students took AI in Spring 2022. b) Every student who takes AI passes it. c) Only one student took AI in Spring 2022. d) No one took AI in Fall 2021.
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...
Related questions
Question
Refer to following image and provide complete solutions with explanations!
Transcribed Image Text:1. Decide whether each of the following sentences is valid, satisfiable or unsatisfiable.
a) Smoke Fire
b) SmokeSmoke
c) Smoke v Fire v-Fire
d) (Smoke Fire) → (→Smoke →→Fire)
2. Given the following sentences in propositional calculus:
1. (ru)
2. (u →→w)
3. (rw)
Use resolution refutation to prove →w.
Joe doesn't get wet
3. Represent the following sentences in first-order logic, using a consistent vocabulary
that you define:
If it rains, Joe brings his umbrella
If Joe has an umbrella, he doesn't get wet
If it doesn't rain, Joe doesn't get wet
a) Some students took AI in Spring 2022.
b) Every student who takes AI passes it.
c) Only one student took AI in Spring 2022.
d) No one took AI in Fall 2021.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 13 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
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
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
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
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning