Part I: Proving that an argument is valid using rules of inference1.Write each of the following arguments in argument form. Then, use therules 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 lecturerecording. 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," andR(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 thehomework 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 permissionfrom 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 takenCS 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 inthis class has taken CS 111.

The rules of inference are a logical framework or guide that draws a conclusion from premises (or…

Answered: rules of inference to show that each…

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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Size of sample space L.A An eleven-sided dice is rolled and a five-sided is tossed. Considering this as a probability experiment, what is the size of the sample space? An Event In the context of the probability experiment just described. Consider the event in which the two numbers on the two dice add to 12. What is the size of this set? 1.B Probability of an event (1/2) What is the probability of the event just described? Write your answer as a fraction of integers. For example, if the answer were 17/20 then enter 17/20 with no spaces or other symbols. You may reduce the fraction by cancelling factors common to the numerator and denominator but you do not need to do this. 1.C Probability of an event (2/2) What is the probability that upper faces on the two dice add to fifteen? Write your answer as a fraction of integers. For example, if the answer were 17/20 then enter 17/20 with no spaces or other symbols. You may reduce the fraction by cancelling factors common to the numerator and…
D. Determine if valid or invalid. Using Rules of Inference. 28. If you play golf during a thunderstorm, you’ll get hit by lightning. You didn’t get hit by lightning. Therefore, you didn’t play golf during a thunderstorm.
Let q = and r = 8=q+rands= be two rational numbers written in lowest terms. Let be written in lowest terms. Assume that s is not 0. Prove or disprove the following two statements. a. If b and d are odd, then f is odd. b. If b and d are even, then f is even.
Is (X and Y) or (Z and W) a tautology? Tautology means for any assignment, the formula evaluates to true. Yes O No
Postulate: If it rains the sidewalk will be wet. Observation: the sidewalk is wet. From this, we can deduce which of the following: a. Nothing b. No answer text provided. c. No answer text provided. d. It rained
VII. Using rules construct deductions to prove that the following are valid 1.1-L&-S 2 (Pv Q) -L 2.1.(R v Q) & S 2. (R v Q)-P 3. PvT
Which statement is NOT correct? O A. Every WFF is equivalent to a WFF in prenex normal form. B. Skolemization does not change the meaning of sentences. C. Skolemization generates equisatisfiable sentences. D. A formula in Skolem form does not have existentially quantified variables.
Find a proposition with three variables p,q and r that is true when p and q are true, and r is false, and false otherwise. Construct a truth table to verify your answer
For the following conditional statements, write (i) the contrapositive of the statement (ii) the converse of the statement, and (iii) the negation of the statement.In part (a), your answer should be written in English (not in propositional logic).For (a), you might have to use DeMorgan’s Laws as part of the process.(a) (6 marks) If the schools are open and the roads are safe, then the game is not cancelled

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