1. Using rules of inference, laws of logical equivalences, and other definitions taught in class, show that the premises conclude with "It is not true that "If I turn in my homework early, then I will go to sleep early"" Be sure to define all propositional variables for full credit. Remember, it is possible that you will use all premises, but it is also possible that some are not needed a.) Today is Friday and Papa Johns is on fire. b.) I will win a chess match if today is a Friday or I do not watch a movie. c.) I sleep early only if I do not win a chess match.

1. Using rules of inference, laws of logical equivalences, and other definitions taught in class, show that the premises conclude with "It is not true that "If I turn in my homework early, then I will go to sleep early"" Be sure to define all propositional variables for full credit. Remember, it is possible that you will use all premises, but it is also possible that some are not needed a.) Today is Friday and Papa Johns is on fire. b.) I will win a chess match if today is a Friday or I do not watch a movie. c.) I sleep early only if I do not win a chess match.

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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Convert to proposition (math logic) If students understand mathematics, then they will be interested to learn more. Feathers protect the bird against the weather, moreover, feathers insulate the bird against loss of heat. If the cake gets hot then the icing melts and if the icing melts, then the cake cannot be used at wedding reception. The school principal already gave you a warning, moreover his father and mother are both not happy about it.
Solve the following puzzle by translating statements into logical expressions and reasoning fromthese expressions.Four friends have been identified as suspects for an unauthorized access into a computer system.They have made statements to the investigating authorities.1-Alice said Carlos did it.2-John said I did not do it.3-Carlos said Diana did it.4-Diana said Carlos lied when he said that I did it.If the authorities also know that exactly one of the four suspects is telling the truth, who didit?
Translate the English sentence to propositional logic. a) Every student majoring in Cumputer science need to visit the science museum b) Use the De Morgan’s law to find the negation of “Some students has visited the science museum.”
Mathematical Logic. First-order or predicate logic Translate each English statement into the specified first-order language. Try to make the end result as readable as possible. a) (i) Some people can be fooled all the time. (ii) All people can be fooled some of the time. (iii) You cannot fool all the people all the time. (∀, for all things; ?, is a person; ?, is a time; ???, ? can be fooled into ?. One or more of the above statements may be ambiguous, in which case more than one translation is needed .) b) (i) Alvarez cannot perform all jobs well. (ii) Alvarez cannot do any job well. (∀, for all things; ?, is a job; ?, Alvarez; ???, ? can do ? well.) Explain your answer. Thank you very much.
9. For each of these collections of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion from the premises. a) "If I take the day off, it either rains or snows." "I took Tuesday off or I took Thursday off." "It was sunny on Tuesday." "It did not snow on Thursday." b) "If I eat spicy foods, then I have strange dreams." "I have strange dreams if there is thunder while I sleep." "I did not have strange dreams." c) "I am either clever or lucky." "I am not lucky." "If I am lucky, then I will win the lottery." d) "Every computer science major has a personal com- puter." "Ralph does not have a personal computer." "Ann has a personal computer." e) "What is good for corporations is good for the United States." "What is good for the United States is good for you." "What is good for corporations is for you to buy lots of stuff." f) "All rodents gnaw their food." "Mice are rodents." "Rabbits do not gnaw their food." "Bats are…
Determine whether the following argument is valid. Justify your answer by firsttranslating each statement into propositional logic to obtain the form of the argument. Then prove thatthe form is valid or not valid.
1. Given the following, can you prove the unicorn is mythical? How about Magi- cal? and Horned? (adapted from Barwise and Etchemendy (1993)). if the unicorn is mythical, then it is immortal, but if it is not mythical, then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is horned. The unicorn is magical if it is horned. 2. Which of the following are correct? (a) False E True (b) (A A B) E (A + B) (c) A + BEAVB (d) A + BE¬AV B (e) (A V B) ^ (¬A V B) is satisfiable
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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
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Private terms are those one of which signifies a perfection and the other of which denies a perfection in a subject which naturally ought to possess it. a. Life – death b. Coffee – cream c. Bread – butter d. Mother – child e. All of the above
Four mathematicians have a conversation, as follows: ALICE: I am insane. BOB: I am pure. CHARLES: I am applied. DOROTHY: I am sane. ALICE: Charles is pure. BOB: Dorothy is insane. CHARLES: Bob is applied. DOROTHY: Charles is sane. You are also given the following information: Pure mathematicians tell the truth about their beliefs. Applied mathematicians lie about their beliefs. Sane mathematicians' beliefs are correct. Insane mathematicians' beliefs are incorrect. With the preceding clues, classify the four mathematicians as applied or pure, and insane or sane. Briefly explain your logic.