Propositional logic exercises with answers

    • [PDF File]Discrete Maths: Exercises & Solutions

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      Propositional logic, studied in Sections 1.1–1.3, cannot adequately express the meaning of all statements in mathematics and in natural language. For example, suppose that we know that “Every computer connected to the university network is functioning properly.” No rules of propositional logic allow us to conclude the truth of the statement

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    • [PDF File]Propositional Logic{ Solution

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      encode the facts in propositional logic and implement a resolution procedure on your computer. Since you do not make any mistakes, the computer will give you the correct answer. You ask the computer whether the facts entail that Amy is a truth-teller. a) The computer tells you that the facts entail that Amy is a truth-teller. Since

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    • [PDF File]MATHEMATICAL LOGIC EXERCISES - UniTrento

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      Propositional Logic Exercise 2.6. - Use the truth tables method to determine whether the formula ’: p^:q!p^q is a logical consequence of the formula : :p.

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    • [PDF File]Solutions of the exercises on Propositional and …

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      Solutions of the exercises on Propositional and Predicate Logic April 13, 2007 Exercises on slide 19 Exercise 1 Show [p∧(p → q)] → q is a tautology. Solution Let us make a truth table for this proposition: p q p → q p∧(p → q) [p∧(p → q)] → q T T T T T T F F F T F T T F T F F T F T

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    • [PDF File]Propositional Logic - Harvard University

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      Exercise 1: Translate the following sentences into propositional logic. Note that some of the questions could have multiple answers. (4)a.It is not the case that Guy comes if Peter or Harry comes. b.John is not only stupid but nasty too. c.Nobody laughed or applauded. d.Charles and Elsa are brother and sister or nephew and niece. 2

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    • [PDF File]Part II: Propositional Logic Homework Problems

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      Translate the following English sentences into propositional logic: 1.If the Astros win the series (”AW”), then pigs will fly (”PF”). 2.Pigs will not fly, and/or bacon will be free (”BF”). 3.The Astros will win the series, or bacon will be free (but not both). Solution: (solution set will be posted later) Exercise 5: [practice]

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    • [PDF File]Classical Propositional Logic - Answers to Exercises 1

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      Classical Propositional Logic - Answers to Exercises 1 Overview of Logic and Computation Australian National University Exercise 1. For each of the formulas below, do the following: 1.using the tableau calculus check if it is valid. If it is not go to point 2 of this exercise; 2.using truth tables determine if it is satis able.

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    • [PDF File]A Exercises Exercise Sheet 1: Propositional Logic

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      A Exercises Exercise Sheet 1: Propositional Logic 1. Let p stand for the proposition“I bought a lottery ticket”and q for“I won the jackpot”. Express the following as natural English sentences: (a) ¬p (b) p∨ q (c) p∧ q (d) p ⇒ q (e) ¬p ⇒ ¬q (f) ¬p∨ (p∧ q) 2.

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    • [PDF File]Propositional Logic: exercises

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      Propositional Logic: exercises 1. Prove that p∧¬pis unsatisfiable 2. Prove that p∨¬pis a tautology 3. Write the truth table of the following two formula (p∧¬(q∨r)) and (¬p∨(q∨r)). Say for each one if it is a tautology, satisfiable or contradiction. Say if one is a logical consequence of the other 4. Let F and Gbe two formula.

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    • [DOC File]Florida Atlantic University | Florida Atlantic University

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      The course will begin with a quick review of the symbolization techniques of propositional logic and of truth-functional operators. This will be followed by a discussion of the methods of direct proof, conditional proof, and indirect proof in propositional logic. ... the professor conveys information and answers questions, but it is the student ...

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    • [DOCX File]1 - EIU

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      Every student has FIFTEEN FREE PASSES for missed online assignments or assignments that you wish to redo for a better grade.A free pass covers one section, for example. 3.2 or 1.1. In order to request a free pass please include which pass, which section and missed date, i.e. Pass#3 section 3.1 2/15.

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    • [DOC File]Logic Syllabus--William and Mary

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      This course is an introduction to symbolic logic. We will cover propositional logic (the logic of sentences) and predicate logic (the logic of parts of sentences), and, if time permits, we will dip into some metalogical issues, such as the soundness and completeness of our logical system. ... (which has the answers to the unstarred exercises ...

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    • [DOC File]EXAM 1 (Mid-term, tentatively October 12.)

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      Exam I (30%) --The exam includes multiple choice, true/false questions and short answers to logical problems. 2. Quizzes (30%) –There are approximately 6 quizzes that are given at the first 10 minutes of the class session.

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    • [DOCX File]Homework: MATH 201

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      Homework: MATH 201. Homework 0: Due: Tuesday, September 12th Briefly relate (in one or two paragraphs) information about yourself that will help me get to know you. If you wish, you may let the following questions serve as a guide: When did you take Math 161 and 162 (or their equivalents)?; why are you taking Math 201 now?

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    • [DOC File]Philosophy 045

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      The formal system we shall be studying is called propositional logic. Roughly, a proposition is the content of, or what is referred to by, a declarative sentence. Grammatically, we can test for propositions by asking ourselves if it would be suitable to put the proposition after the …

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    • [DOC File]Discrete Mathematics - MGNet

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      Propositional logic is pretty limited. Almost anything you really are interested in requires a more sophisticated form of logic: predicate logic with quantifiers (or predicate calculus). Definition: P(x) is a propositional function when a specific value x is substituted …

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    • [DOC File]“MATHEMATICAL PHYSICS” AND “PHYSICAL MATHEMATICS”:

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      The course “Introduction to Mathematical Logic” (32 h lectures + 32 h exercises + 56 h independent work) is compulsary at the Faculty of Mathematics and Informatics of the University of Tartu. In 1987-1991, we designed four programs for the exercises: Truth-Table Checker, Formula Manipulation Assistant, Proof Editor and Turing Interpreter.

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    • [DOCX File]Homework: MATH 201

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      (a) In propositional logic, modus ponendo ponens (Latin for "the way that affirms by affirming"; generally abbreviated to MP or modus ponens) or implication elimination is a rule of inference. It can be summarized as " p implies q and p is asserted to be true, so therefore q must be true," viz, p ∧ p⇒q ⇒q.

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    • [DOC File]To be returned to: - The Logic Manual

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      Sample answers for HT13 Elementary logic questions collection (Thanks to Anna Mahtani and Volker Halbach for proof reading the question paper. Complaints, corrections and comments to Gail Leckie at Mansfield.) 1A (a) Formalize the following into a valid argument in L1 (the propositional calculus), noting any difficulties or points of interest ...

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