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.

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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