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(b) Let F(x) be "x is friendly," T(x) be "x learns a trick," and S(r) be "x is shy," where the domain consists of all dogs. Every dog who is friendly learns a trick. Every dog is friendly or shy. Therefore, every dog who isn't shy learns a trick. Write each of the following arguments in argument form (i.e., using propositions, predicates, quantifiers, and logical operators). Then, use the rules of inference and the laws of propositional logic to prove that each argument is valid. You must indicate the name of the rule used in each step of the proof. EXAMPLE: Let r be "I run" and let e be "I eat." If I run, then I eat. I run. Therefore, I run and I eat. hypothesis hypothesis Answer: 1. re re 2. r r 3. e .. гле modus ponens (1, 2) 4. гле conjunction (2, 3)

(b) Let F(x) be "x is friendly," T(x) be "x learns a trick," and S(r) be "x is shy," where the domain consists of all dogs. Every dog who is friendly learns a trick. Every dog is friendly or shy. Therefore, every dog who isn't shy learns a trick. Write each of the following arguments in argument form (i.e., using propositions, predicates, quantifiers, and logical operators). Then, use the rules of inference and the laws of propositional logic to prove that each argument is valid. You must indicate the name of the rule used in each step of the proof. EXAMPLE: Let r be "I run" and let e be "I eat." If I run, then I eat. I run. Therefore, I run and I eat. hypothesis hypothesis Answer: 1. re re 2. r r 3. e .. гле modus ponens (1, 2) 4. гле conjunction (2, 3)

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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(b) Let F(x) be "x is friendly," T(x) be "x learns a trick," and S(r) be "x is shy," where the domain consists of all dogs. Every dog who is friendly learns a trick. Every dog is friendly or shy. Therefore, every dog who isn't shy learns a trick.
Transcribed Image Text:(b) Let F(x) be "x is friendly," T(x) be "x learns a trick," and S(r) be "x is shy," where the domain consists of all dogs. Every dog who is friendly learns a trick. Every dog is friendly or shy. Therefore, every dog who isn't shy learns a trick.
Write each of the following arguments in argument form (i.e., using propositions, predicates, quantifiers, and logical operators). Then, use the rules of inference and the laws of propositional logic to prove that each argument is valid. You must indicate the name of the rule used in each step of the proof. EXAMPLE: Let r be "I run" and let e be "I eat." If I run, then I eat. I run. Therefore, I run and I eat. hypothesis hypothesis Answer: 1. re re 2. r r 3. e .. гле modus ponens (1, 2) 4. гле conjunction (2, 3)
Transcribed Image Text:Write each of the following arguments in argument form (i.e., using propositions, predicates, quantifiers, and logical operators). Then, use the rules of inference and the laws of propositional logic to prove that each argument is valid. You must indicate the name of the rule used in each step of the proof. EXAMPLE: Let r be "I run" and let e be "I eat." If I run, then I eat. I run. Therefore, I run and I eat. hypothesis hypothesis Answer: 1. re re 2. r r 3. e .. гле modus ponens (1, 2) 4. гле conjunction (2, 3)
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