(b) Let propositions p, q, r, s,t be defined as: • p: It is warm outside • q: I am wearing a jacket • r: It is winter • s: I am drinking tea • 1: It gets dark before 4PM Assume the following statements: If it is not winter, then I am drinking tea • If it is not warm outside, I am wearing a jacket • If it is winter, then it is not warm outside and it gets dark before 4PM . I am not drinking tea Using the rules of inference, prove that I am wearing a jacket. State which rule you are using at each step. You do not need to draw a proof tree.

(b) Let propositions p, q, r, s,t be defined as: • p: It is warm outside • q: I am wearing a jacket • r: It is winter • s: I am drinking tea • 1: It gets dark before 4PM Assume the following statements: If it is not winter, then I am drinking tea • If it is not warm outside, I am wearing a jacket • If it is winter, then it is not warm outside and it gets dark before 4PM . I am not drinking tea Using the rules of inference, prove that I am wearing a jacket. State which rule you are using at each step. You do not need to draw a proof tree.

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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Question
Consider the following true propositions:• p : The applicant has passed the learner permit test.• q : The applicant has passed the road test.• r : The applicant is allowed a driver’s license.For each of the following sentences write,symbolically, the compound proposition that correspondstothe given sentence in English asit is written (do not change the order or form of the expression).a) The applicant did not pass the road test but passed the learner permit test.b) If the applicant passes the learner permit test and the road test, then the applicant is allowed adriver’s license.c) Passing the learner permit test and the road test are necessary for being allowed a driver’slicense.d) The applicant passed either the learner permit test or the road test, but not both.e) It is not true that the applicant does not pass the road test and is allowed a driver’s license.
3. A) Let x and y be the propositions x: It is extremely hot. y: It is sunny. Write these propositions using x and y and logical connectives: a) It is extremely hot but not sunny. b) It is not extremely hot and it is not sunny. c) It is either sunny or extremely hot (or both). d) If it is extremely hot, it is also sunny. e) Either it is extremely hot or it is sunny, but it is not sunny if it is extremely hot.
Let p, q, and r represent the following statements: p: The first ball is red. q: The second ball is white. r: The third ball is blue. Which would be the correct English statement for the symbolic form (¬¬p ∧∧ q) →→ r ? Group of answer choices A .If the first ball is red or the second ball is white, then the third ball is blue. B. If the first ball is not red or the second ball is white, then the third ball is blue. C .If the first ball is not red and the second ball is white, then the third ball is blue. D. If the first ball is red and the second ball is white, then the third ball is blue.
1. 2. Let N, H, S, D, R, J, and B be the propositions: N: Mr. Smith is the brakeman's next-door neighbor H: Mr. Smith lives halfway between Detroit and Chicago S: Mr. Smith lives in Chicago D: Mr. Robinson lives in Detroit R: Mr. Robinson lives in Chicago J: Mr. Jones lives in Chicago B: Jones is the brakeman Write the proposition below using N, H, S, D, R, J, B, and logical operators. OHS OHV~S If Mr. Smith lives halfway between Detroit and Chicago, then he does not live in Chicago. O~H~S OH S Let N, H, S, D, R, J, and B be the propositions: N: Mr. Smith is the brakeman's next-door neighbor H: Mr. Smith lives halfway between Detroit and Chicago S: Mr. Smith lives in Chicago D: Mr. Robinson lives in Detroit R: Mr. Robinson lives in Chicago J: Mr. Jones lives in Chicago B: Jones is the brakeman Write the proposition below using N, H, S, D, R, J, B, and logical operators. ORD ODR O DV~S ODS If Mr. Robinson lives in Detroit, then he does not live in Chicago.
For each of the following statements, let the domain be all animals in the world. 1. Express each of the statements using quantifiers and propositional functions. 2. Form the negation of the statement so that no negation is to the left of the quantifier. 3. Express the negation in simple English. (Do not simply use the words “it is not the case that..."). (a) All dogs have fleas (b) There is a horse that can add. (c) Every koala can climb. (d)No monkey can speak French. (e) There exists a pig that can swim and catch fish.
Question 37 The correct statements are: If both L and ¬L are in D, then L must be also in SD. If both L and ¬L are in D, then ¬L must be also in SD. If both L and ¬L are in SD, then L must be also in D. If both L and ¬L are in SD, then ¬L must be also in D.
Let p, q, and r be the propositions: p: You have the flu. q : You miss the final examination. r: You pass the course. The proposition ¬q → r as an English sentence is: (a) You do not miss the final examination if and only if you pass the course. (b) You do not pass the course if and only if you miss the final examination. (c) I won the million dollar jackpot on Friday, and so I will not have flu and I want to miss the final examination. (d) I hope the final examination will not be a lottery.
Q: The propositional variables b, v, and s represent the propositions: b: Alice rode her bike today. v: Alice overslept today. s: It is sunny today. Select the logical expression that represents the statement: “Alice rode her bike today only if it was sunny today and she did not oversleep.” b→(s→¬v) 2. b→(s∧¬v) 3. s∧(¬v→b) 4. (s∧¬v)→b Group of answer choices b→(s∧¬v) b→(s→¬v) s∧(¬v→b) (s∧¬v)→b 2); The following two statements are logically equivalent (p → q) ∧ (r → q) and (p ∧ r) → q Group of answer choices True False
Q: The propositional variables b, v, and s represent the propositions: b: Alice rode her bike today. v: Alice overslept today. s: It is sunny today. Select the logical expression that represents the statement: “Alice rode her bike today only if it was sunny today and she did not oversleep.” b→(s→¬v) 2. b→(s∧¬v) 3. s∧(¬v→b) 4. (s∧¬v)→b Group of answer choices A): b→(s∧¬v) B): b→(s→¬v) C): s∧(¬v→b) D): (s∧¬v)→b
Let A, S, R be the propositions:A : Ahmed passed the ExamS : Samir passed the ExamR : Rami passed the ExamWrite the following propositions using the three propositions A, S, and R and logicalconnectives : 1) At least one passed the exam2) At least two passed the exam3) At most two passed the exam
Consider the following narration: If gender equality is to be achieved then patriarchy must be dismantled. If patriarchy is dismantled then matriarchy should be discouraged. If matriarchy is discouraged then gender equality is not to be achieved. Patriarchy is not going to be dismantled. Therefore, gender equality is not to be achieved a) Encode the argument in Propositional Calculus. b) As a result of a) above, use logical rules of inference to show that the given argument is sound/valid. HINT: For any statement forms, P and Q P ---> Q = ¬Q ---> ¬P