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rules of inference to show that each argument is valid. a. Let p be the proposition "I attend the lecture," q be "I watch the lecture recording," and r be "I do well on the quiz." If I attend the lecture, then I do well on the quiz. I attend the lecture or watch the lecture recording I did not watch the lecture recording Therofore Ldid well on the qui,

rules of inference to show that each argument is valid. a. Let p be the proposition "I attend the lecture," q be "I watch the lecture recording," and r be "I do well on the quiz." If I attend the lecture, then I do well on the quiz. I attend the lecture or watch the lecture recording I did not watch the lecture recording Therofore Ldid well on the qui,

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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Part I: Proving that an argument is valid using rules of inference 1. Write each of the following arguments in argument form. Then, use the rules of inference to show that each argument is valid. a. Let p be the proposition "/ attend the lecture," q be “I watch the lecture recording." and r be "I do well on the quiz." If I attend the lecture, then I do well on the quiz. I attend the lecture or watch the lecture recording. I did not watch the lecture recording. Therefore, I did well on the quiz. b. Let P(x) be "x attended the lecture," Q(x) be "x submitted the homework assignment," and R(x) be "x passed the exam," where the domain consists of all students in this class. Every student in this class who did not attend the lecture or did not submit the homework assignment did not pass the exam. Bob, who is a student in this class, passed the exam. Therefore, Bob attended the lecture. c. Let P(x) be "x has taken CS 109," Q(x) be “x has taken CS 111," and R(x) be "x has permission from the instructor to enroll in this class," where the domain consists of all students in this class. Every student in this class has taken CS 111 or CS 109. Every student who has not taken CS 111 but has taken CS 109, has permission from the instructor to enroll in this class. Therefore, every student who does not have permission from the instructor to enroll in this class has taken CS 111.
Transcribed Image Text:Part I: Proving that an argument is valid using rules of inference 1. Write each of the following arguments in argument form. Then, use the rules of inference to show that each argument is valid. a. Let p be the proposition "/ attend the lecture," q be “I watch the lecture recording." and r be "I do well on the quiz." If I attend the lecture, then I do well on the quiz. I attend the lecture or watch the lecture recording. I did not watch the lecture recording. Therefore, I did well on the quiz. b. Let P(x) be "x attended the lecture," Q(x) be "x submitted the homework assignment," and R(x) be "x passed the exam," where the domain consists of all students in this class. Every student in this class who did not attend the lecture or did not submit the homework assignment did not pass the exam. Bob, who is a student in this class, passed the exam. Therefore, Bob attended the lecture. c. Let P(x) be "x has taken CS 109," Q(x) be “x has taken CS 111," and R(x) be "x has permission from the instructor to enroll in this class," where the domain consists of all students in this class. Every student in this class has taken CS 111 or CS 109. Every student who has not taken CS 111 but has taken CS 109, has permission from the instructor to enroll in this class. Therefore, every student who does not have permission from the instructor to enroll in this class has taken CS 111.
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