FIRST PUBLIC EXAMINATION. Preliminary Examination in Philosophy, Politics and Economics INTRODUCTION TO PHILOSOPHY LONG VACATION 2014
|
|
- Edwina Barnett
- 5 years ago
- Views:
Transcription
1 CPPE 4266 FIRST PUBLIC EXAMINATION Preliminary Examination in Philosophy, Politics and Economics INTRODUCTION TO PHILOSOPHY LONG VACATION 2014 Thursday 4 September 2014, 9.30am pm This paper contains three sections: Logic; General Philosophy; and Moral Philosophy. You must answer FOUR questions, including at least one question from each section. You may answer your fourth question from any section. In the Logic section, questions 1 and 2 are of an elementary and straightforward nature; the remaining questions are more demanding. You may answer only one of questions 1 and 2 (but are not obliged to attempt either). The numbers in the margin in the Logic section indicate the marks which the Moderators expect to assign to each part of the question. IMPTANT You must use a separate booklet for your answers to each section. Write your CANDIDATE NUMBER on each booklet. DO NOT write your name. Do NOT turn over until told that you may do so
2 SECTION A: LOGIC (Please use a separate booklet for each section) 1. (a) Define what it is for a relation R on a set S to be (i) reflexive; (ii) symmetric; (iii) transitive; (iv) an equivalence relation. [4] (b) A relation R on a set S is serial if for every a in S there is a (not necessarily distinct) b in S such that a, b is in R. (i) Let S be the set of human beings currently alive. Give an example of a relation R on S that is serial. Briefly justify your answer. (ii) Let S once more be the set of human beings currently alive. Give an example of a relation R on S that is not serial. Briefly justify your answer. (iii) Suppose that a relation R on a set S is reflexive. Must R be serial on S? Justify your answer. (iv) Suppose that a relation R on a set S is symmetric, transitive and serial. Must R also be reflexive on S? Justify your answer. (v) Suppose that a relation R on a finite set S is transitive and serial. Must there be an element a in S such that a, a is in R? Justify your answer. [4] (c) (i) Suppose that the set S has one element and that R is a relation on S. Must R be an equivalence relation? Justify your answer. (ii) Suppose that the set S has one element and that R 1 and R 2 are distinct relations on S. Must at least one of R 1 or R 2 be an equivalence relation on S? Justify your answer. (ii) Suppose that the set S has two elements. How many distinct equivalence relations are there on S?
3 2. (a) Define what it is for an L 1 -sentence to be an L 1 -tautology. (b) Using truth-tables or otherwise, determine whether the following are L 1 - tautologies: (i) (P P) (Q Q) (ii) (P P) (Q R) (iii) ((P Q) R) (P (Q R)) [8] (c) (i) Suppose that 1 and 2 are L 1 -tautologies that do not share a sentence letter. Must 1 2 be an L 1 -tautology? Justify your answer. (ii) Suppose that 1 and 2 are L 1 -sentences that do not share a sentence letter. If 1 2 is an L 1 -tautology, what can you say about each of 1 and 2? Justify your answer. [5] (d) Asked about the relation of logical consequence in L 1, a student says: means that if then, which may be formalised as. Explain in detail where the student s argument goes wrong. [7] 3. (a) State the natural deduction rules for propositional logic (the language L 1 ). You should justify any conditions imposed on the application of a rule. [10] (b) State the natural deduction rules for predicate logic without identity (the language L 2 ) supplementary to the ones stated in (a). You should justify any conditions imposed on the application of a rule. [12] (c) State the natural deduction rules for predicate logic with identity (the language L = ) supplementary to the ones stated in (a) and (b). You should justify any conditions imposed on the application of a rule TURN OVER
4 4. (a) Which of the following English connectives are truth-functional? Justify your answers. (i) A unless B. (ii) If John remembers that A then it was the case that A. (iii) A because B. (iv) If it were the case that A then it would be the case that B. [12] (b) Formalise the following sentences in predicate logic with identity (the language L = ), including a dictionary. (i) (ii) (iii) (iv) Abraham likes a subject only if it s easy. Two queens of England have been called Elizabeth. The three musketeers surrounded the statue. To lose one parent is a misfortune; to lose two is carelessness. [13] 5. For each claim below, either provide a natural deduction proof showing that the entailment holds, or else provide a counterexample to show that it does not. (i) {Q, P Q } P (ii) { (P Q) } Q (iii) {P 1 (P 2 ( P 3 P 4 )), P 4 (P 1 P 2 )} ( P 1 P 2 P 3 P 4 ) (iv) { x(px Qx)} x(qx Px) (v) { x y(rxy Ryx), x y z(z = x z = y)} xrxx (vi) { x y(rxy Ryx), x y z((rxy Ryz) Rxz)} xrxx [25]
5 SECTION B: GENERAL PHILOSOPHY (Please use a separate booklet for each section) 6. EITHER (a) Is there a satisfactory way to save the account of knowledge as justified true belief from Gettier s challenge? (b) Do you know whether or not you are a brain in a vat? 7. EITHER (a) What are Hume s concerns about induction? Does he answer them? (b) Do you know whether the laws of nature will still be the same at the end of this exam as they were when you started it? 8. EITHER (a) Does Descartes offer a compelling argument for substance dualism in the 2 nd Meditation? (b) What does Jackson s thought experiment about Mary establish? 9. EITHER (a) Is there any more to freedom than acting without coercion? (b) I want you to perform a certain action A. If you decide to do A, then I will do nothing. But if you do not decide to do A, then I will press a button which makes you do A. You decide to do A, so I do nothing. What does this case tell us about what it is to be free? TURN OVER
6 10. EITHER (a) Does Locke provide good reasons for thinking the diachronic identity conditions for human beings differ from those of persons? (b) What, if anything, can we learn about personal identity from reflecting on the possibilities of fission and fusion? 11. EITHER (a) Does God s existence follow from God s essence? (b) Does awareness of the suffering inflicted on humans by large scale natural disasters make it irrational to believe in God? SECTION C: MAL PHILOSOPHY (Please use a separate booklet for each section) 12. Since utilitarianism is a philosophy of reform, the fact that its prescriptions so often go against common sense is a mark in its favour, not a mark against it. Is this correct? 13. Should utilitarians look to actual consequences, intended consequences or foreseeable consequences? 14. Are intensity and duration of pleasure any more commensurable with each other than quality and quantity? 15. If Mill is correct that the origin of the notion of justice is connected with the ordinances of law (Utilitarianism, ch.5) what sense can be made of the notion of natural justice? 16. Mill fails to prove utilitarianism because no ethical theory can ever be proven. Discuss. 17. Utilitarianism only compromises the integrity of non-utilitarians. Discuss. [END OF PAPER] LAST PAGE
I thank the author of the examination paper on which sample paper is based. VH
I thank the author of the examination paper on which sample paper is based. VH 1. (a) Which of the following expressions is a sentence of L 1 or an abbreviation of one? If an expression is neither a sentence
More informationCPPE TURN OVER
[4] [1] [4] [16] The solutions are highly incomplete and only intended to give a rough idea. 1. (a) Which of the following expressions is an abbreviation of a sentence of L 1? If an expression is an abbreviation
More information(c) Establish the following claims by means of counterexamples.
sample paper I N T R O D U C T I O N T O P H I L O S O P H Y S E C T I O N A : L O G I C Volker Halbach Michaelmas 2008 I thank the author of the 2008 Trinity Term paper, Andrew Bacon, and Kentaro Fujimoto
More informationInterpretations of PL (Model Theory)
Interpretations of PL (Model Theory) 1. Once again, observe that I ve presented topics in a slightly different order from how I presented them in sentential logic. With sentential logic I discussed syntax
More informationAnnouncements & Such
Branden Fitelson Philosophy 12A Notes 1 Announcements & Such Administrative Stuff HW #6 to be handed back today. Resubs due Thursday. I will be posting both the sample in-class final and the take-home
More informationOverview of Today s Lecture
Branden Fitelson Philosophy 4515 (Advanced Logic) Notes 1 Overview of Today s Lecture Administrative Stuff HW #1 grades and solutions have been posted Please make sure to work through the solutions HW
More informationAI Principles, Semester 2, Week 2, Lecture 5 Propositional Logic and Predicate Logic
AI Principles, Semester 2, Week 2, Lecture 5 Propositional Logic and Predicate Logic Propositional logic Logical connectives Rules for wffs Truth tables for the connectives Using Truth Tables to evaluate
More information2010 Part IA Formal Logic, Model Answers
2010 Part IA Formal Logic, Model Answers 1 Attempt all parts of this question (a) Carefully define the notions of (i) a truth-function A function is a map which assigns exactly one value to each given
More informationOverview of Today s Lecture
Branden Fitelson Philosophy 4515 (Advanced Logic) Notes 1 Overview of Today s Lecture Administrative Stuff HW #1 grades and solutions have been posted Please make sure to work through the solutions HW
More information1A Logic 2015 Model Answers
1A Logic 2015 Model Answers Section A 1. (a) Show each of the following [40]: (i) P Q, Q R, P R P 1 P Q 2 Q R 3 P R 4 P 5 P R, 4 6 P 7 Q DS, 1, 6 8 R DS, 2, 7 9 R 10 I, 8, 9 11 R E, 9, 10 12 P MT, 3, 11
More informationEXERCISES BOOKLET. for the Logic Manual. Volker Halbach. Oxford. There are no changes to the exercises from last year s edition
EXERCISES BOOKLET for the Logic Manual 2017/2018 There are no changes to the exercises from last year s edition Volker Halbach Oxford 21st March 2017 1 preface The most recent version of this Exercises
More informationHomework assignment 1: Solutions
Math 240: Discrete Structures I Due 4:30pm Friday 29 September 2017. McGill University, Fall 2017 Hand in to the mailbox at Burnside 1005. Homework assignment 1: Solutions Discussing the assignment with
More information4 The semantics of full first-order logic
4 The semantics of full first-order logic In this section we make two additions to the languages L C of 3. The first is the addition of a symbol for identity. The second is the addition of symbols that
More informationModal Logic. UIT2206: The Importance of Being Formal. Martin Henz. March 19, 2014
Modal Logic UIT2206: The Importance of Being Formal Martin Henz March 19, 2014 1 Motivation The source of meaning of formulas in the previous chapters were models. Once a particular model is chosen, say
More informationIntroducing Proof 1. hsn.uk.net. Contents
Contents 1 1 Introduction 1 What is proof? 1 Statements, Definitions and Euler Diagrams 1 Statements 1 Definitions Our first proof Euler diagrams 4 3 Logical Connectives 5 Negation 6 Conjunction 7 Disjunction
More informationModal Logic: Exercises
Modal Logic: Exercises KRDB FUB stream course www.inf.unibz.it/ gennari/index.php?page=nl Lecturer: R. Gennari gennari@inf.unibz.it June 6, 2010 Ex. 36 Prove the following claim. Claim 1. Uniform substitution
More informationIntroduction to Proofs
Introduction to Proofs Many times in economics we will need to prove theorems to show that our theories can be supported by speci c assumptions. While economics is an observational science, we use mathematics
More informationINTRODUCTION TO LOGIC 3 Formalisation in Propositional Logic
Introduction INRODUCION O LOGIC 3 Formalisation in Propositional Logic Volker Halbach If I could choose between principle and logic, I d take principle every time. Maggie Smith as Violet Crawley in Downton
More informationMATH 341, Section 001 FALL 2014 Introduction to the Language and Practice of Mathematics
MATH 341, Section 001 FALL 2014 Introduction to the Language and Practice of Mathematics Class Meetings: MW 9:30-10:45 am in EMS E424A, September 3 to December 10 [Thanksgiving break November 26 30; final
More informationChapter 1 Elementary Logic
2017-2018 Chapter 1 Elementary Logic The study of logic is the study of the principles and methods used in distinguishing valid arguments from those that are not valid. The aim of this chapter is to help
More informationELEMENTARY NUMBER THEORY AND METHODS OF PROOF
CHAPTER 4 ELEMENTARY NUMBER THEORY AND METHODS OF PROOF Copyright Cengage Learning. All rights reserved. SECTION 4.6 Indirect Argument: Contradiction and Contraposition Copyright Cengage Learning. All
More informationUniversity of Illinois at Chicago Department of Computer Science. Final Examination. CS 151 Mathematical Foundations of Computer Science Fall 2012
University of Illinois at Chicago Department of Computer Science Final Examination CS 151 Mathematical Foundations of Computer Science Fall 01 Thursday, October 18, 01 Name: Email: Print your name and
More informationDescription Logics. Foundations of Propositional Logic. franconi. Enrico Franconi
(1/27) Description Logics Foundations of Propositional Logic Enrico Franconi franconi@cs.man.ac.uk http://www.cs.man.ac.uk/ franconi Department of Computer Science, University of Manchester (2/27) Knowledge
More informationTHE LOGIC OF QUANTIFIED STATEMENTS. Predicates and Quantified Statements I. Predicates and Quantified Statements I CHAPTER 3 SECTION 3.
CHAPTER 3 THE LOGIC OF QUANTIFIED STATEMENTS SECTION 3.1 Predicates and Quantified Statements I Copyright Cengage Learning. All rights reserved. Copyright Cengage Learning. All rights reserved. Predicates
More informationFinal Exam Theory Quiz Answer Page
Philosophy 120 Introduction to Logic Final Exam Theory Quiz Answer Page 1. (a) is a wff (and a sentence); its outer parentheses have been omitted, which is permissible. (b) is also a wff; the variable
More informationINTRODUCTION TO LOGIC 8 Identity and Definite Descriptions
8.1 Qualitative and Numerical Identity INTRODUCTION TO LOGIC 8 Identity and Definite Descriptions Volker Halbach Keith and Volker have the same car. Keith and Volker have identical cars. Keith and Volker
More informationFinal Exam (100 points)
Final Exam (100 points) Honor Code: Each question is worth 10 points. There is one bonus question worth 5 points. In contrast to the homework assignments, you may not collaborate on this final exam. You
More informationSymbolic Logic 3. For an inference to be deductively valid it is impossible for the conclusion to be false if the premises are true.
Symbolic Logic 3 Testing deductive validity with truth tables For an inference to be deductively valid it is impossible for the conclusion to be false if the premises are true. So, given that truth tables
More informationThe Natural Deduction Pack
The Natural Deduction Pack Alastair Carr March 2018 Contents 1 Using this pack 2 2 Summary of rules 3 3 Worked examples 5 31 Implication 5 32 Universal quantifier 6 33 Existential quantifier 8 4 Practice
More informationINTRODUCTION TO LOGIC 8 Identity and Definite Descriptions
INTRODUCTION TO LOGIC 8 Identity and Definite Descriptions Volker Halbach The analysis of the beginning would thus yield the notion of the unity of being and not-being or, in a more reflected form, the
More informationMathematical Logic Part Three
Mathematical Logic Part Three Recap from Last Time What is First-Order Logic? First-order logic is a logical system for reasoning about properties of objects. Augments the logical connectives from propositional
More informationWilliamson s Modal Logic as Metaphysics
Williamson s Modal Logic as Metaphysics Ted Sider Modality seminar 1. Methodology The title of this book may sound to some readers like Good as Evil, or perhaps Cabbages as Kings. If logic and metaphysics
More informationPhil Introductory Formal Logic
Phil 134 - Introductory Formal Logic Lecture 7: Deduction At last, it is time to learn about proof formal proof as a model of reasoning demonstrating validity metatheory natural deduction systems what
More informationDiscrete Mathematics and Its Applications
Discrete Mathematics and Its Applications Lecture 1: The Foundations: Logic and Proofs (1.3-1.5) MING GAO DASE @ ECNU (for course related communications) mgao@dase.ecnu.edu.cn Sep. 19, 2017 Outline 1 Logical
More informationMAT2345 Discrete Math
Fall 2013 General Syllabus Schedule (note exam dates) Homework, Worksheets, Quizzes, and possibly Programs & Reports Academic Integrity Do Your Own Work Course Web Site: www.eiu.edu/~mathcs Course Overview
More informationFor all For every For each For any There exists at least one There exists There is Some
Section 1.3 Predicates and Quantifiers Assume universe of discourse is all the people who are participating in this course. Also let us assume that we know each person in the course. Consider the following
More informationPhysicalism Feb , 2014
Physicalism Feb. 12 14, 2014 Overview I Main claim Three kinds of physicalism The argument for physicalism Objections against physicalism Hempel s dilemma The knowledge argument Absent or inverted qualia
More informationWhy Learning Logic? Logic. Propositional Logic. Compound Propositions
Logic Objectives Propositions and compound propositions Negation, conjunction, disjunction, and exclusive or Implication and biconditional Logic equivalence and satisfiability Application of propositional
More informationExercises. Exercise Sheet 1: Propositional Logic
B 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)
More information6. Conditional derivations
6. Conditional derivations 6.1 An argument from Hobbes In his great work, Leviathan, the philosopher Thomas Hobbes (1588-1679) gives an important argument for government. Hobbes begins by claiming that
More informationCHAPTER 2. FIRST ORDER LOGIC
CHAPTER 2. FIRST ORDER LOGIC 1. Introduction First order logic is a much richer system than sentential logic. Its interpretations include the usual structures of mathematics, and its sentences enable us
More informationFrege s Proofs of the Axioms of Arithmetic
Frege s Proofs of the Axioms of Arithmetic Richard G. Heck, Jr. 1 The Dedekind-Peano Axioms for Arithmetic 1. N0 2. x(nx y.p xy) 3(a). x y z(nx P xy P xy y = z) 3(b). x y z(nx Ny P xz P yz x = y) 4. z(nz
More informationReviewed by Martin Smith, University of Glasgow
1 Titelbaum, M. Quitting Certainties: A Bayesian Framework Modelling Degrees of Belief, Oxford University Press, 2013, 345pp., 40 (hbk), ISBN 978-0-19-965830-5 Reviewed by Martin Smith, University of Glasgow
More informationCHAPTER 6 - THINKING ABOUT AND PRACTICING PROPOSITIONAL LOGIC
1 CHAPTER 6 - THINKING ABOUT AND PRACTICING PROPOSITIONAL LOGIC Here, you ll learn: what it means for a logic system to be finished some strategies for constructing proofs Congratulations! Our system of
More informationTECHNISCHE UNIVERSITEIT EINDHOVEN Faculteit Wiskunde en Informatica. Final exam Logic & Set Theory (2IT61) (correction model)
TECHNISCHE UNIVERSITEIT EINDHOVEN Faculteit Wiskunde en Informatica Final exam Logic & Set Theory (2IT61) (correction model) Thursday November 4, 2016, 9:00 12:00 hrs. (2) 1. Determine whether the abstract
More informationIntroduction to Metalogic
Philosophy 135 Spring 2008 Tony Martin Introduction to Metalogic 1 The semantics of sentential logic. The language L of sentential logic. Symbols of L: Remarks: (i) sentence letters p 0, p 1, p 2,... (ii)
More information1 Propositional Logic
CS 2800, Logic and Computation Propositional Logic Lectures Pete Manolios Version: 384 Spring 2011 1 Propositional Logic The study of logic was initiated by the ancient Greeks, who were concerned with
More informationA Little Deductive Logic
A Little Deductive Logic In propositional or sentential deductive logic, we begin by specifying that we will use capital letters (like A, B, C, D, and so on) to stand in for sentences, and we assume that
More informationMath Introduction to Logic Final Exam
Math 2283 - Introduction to Logic Final Exam Assigned: 2018.11.26 Due: 2018.12.10 at 08:00 Instructions: Work on this by yourself, the only person you may contact in any way to discuss or ask questions
More informationElementary Linear Algebra, Second Edition, by Spence, Insel, and Friedberg. ISBN Pearson Education, Inc., Upper Saddle River, NJ.
2008 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. APPENDIX: Mathematical Proof There are many mathematical statements whose truth is not obvious. For example, the French mathematician
More informationCHAPTER 4 CLASSICAL PROPOSITIONAL SEMANTICS
CHAPTER 4 CLASSICAL PROPOSITIONAL SEMANTICS 1 Language There are several propositional languages that are routinely called classical propositional logic languages. It is due to the functional dependency
More informationOn sets, functions and relations
On sets, functions and relations Chapter 2 Rosalie Iemhoff 1 Contents 1 Relations 3 1.1 Cartesian product.......................... 4 1.2 Disjoint sum............................. 5 1.3 Relations of arbitrary
More informationClass 29 - November 3 Semantics for Predicate Logic
Philosophy 240: Symbolic Logic Fall 2010 Mondays, Wednesdays, Fridays: 9am - 9:50am Hamilton College Russell Marcus rmarcus1@hamilton.edu Class 29 - November 3 Semantics for Predicate Logic I. Proof Theory
More information2. Find all combinations of truth values for p, q and r for which the statement p (q (p r)) is true.
1 Logic Questions 1. Suppose that the statement p q is false. Find all combinations of truth values of r and s for which ( q r) ( p s) is true. 2. Find all combinations of truth values for p, q and r for
More information09 Modal Logic II. CS 3234: Logic and Formal Systems. October 14, Martin Henz and Aquinas Hobor
Martin Henz and Aquinas Hobor October 14, 2010 Generated on Thursday 14 th October, 2010, 11:40 1 Review of Modal Logic 2 3 4 Motivation Syntax and Semantics Valid Formulas wrt Modalities Correspondence
More informationTopic #3 Predicate Logic. Predicate Logic
Predicate Logic Predicate Logic Predicate logic is an extension of propositional logic that permits concisely reasoning about whole classes of entities. Propositional logic treats simple propositions (sentences)
More informationThe Process of Mathematical Proof
1 The Process of Mathematical Proof Introduction. Mathematical proofs use the rules of logical deduction that grew out of the work of Aristotle around 350 BC. In previous courses, there was probably an
More informationLogical Structures in Natural Language: Propositional Logic II (Truth Tables and Reasoning
Logical Structures in Natural Language: Propositional Logic II (Truth Tables and Reasoning Raffaella Bernardi Università degli Studi di Trento e-mail: bernardi@disi.unitn.it Contents 1 What we have said
More informationWarm-Up Problem. Let be a Predicate logic formula and a term. Using the fact that. (which can be proven by structural induction) show that 1/26
Warm-Up Problem Let be a Predicate logic formula and a term Using the fact that I I I (which can be proven by structural induction) show that 1/26 Predicate Logic: Natural Deduction Carmen Bruni Lecture
More informationThe Converse of Deducibility: C.I. Lewis and the Origin of Modern AAL/ALC Modal 2011 Logic 1 / 26
The Converse of Deducibility: C.I. Lewis and the Origin of Modern Modal Logic Edwin Mares Victoria University of Wellington AAL/ALC 2011 The Converse of Deducibility: C.I. Lewis and the Origin of Modern
More informationBarriers to Inference
Barriers to Inference Greg Restall University of Melbourne restall@unimelb.edu.au Page 0 of 53 Gillian Russell Washington University in St Louis grussell@artsci.wustl.edu 27th May, FEW 2005 Hume s Law
More informationSection Summary. Section 1.5 9/9/2014
Section 1.5 Section Summary Nested Quantifiers Order of Quantifiers Translating from Nested Quantifiers into English Translating Mathematical Statements into Statements involving Nested Quantifiers Translated
More informationA Little Deductive Logic
A Little Deductive Logic In propositional or sentential deductive logic, we begin by specifying that we will use capital letters (like A, B, C, D, and so on) to stand in for sentences, and we assume that
More informationLogical Reasoning. Chapter Statements and Logical Operators
Chapter 2 Logical Reasoning 2.1 Statements and Logical Operators Preview Activity 1 (Compound Statements) Mathematicians often develop ways to construct new mathematical objects from existing mathematical
More informationLearning Goals of CS245 Logic and Computation
Learning Goals of CS245 Logic and Computation Alice Gao April 27, 2018 Contents 1 Propositional Logic 2 2 Predicate Logic 4 3 Program Verification 6 4 Undecidability 7 1 1 Propositional Logic Introduction
More informationLogic: Propositional Logic Truth Tables
Logic: Propositional Logic Truth Tables Raffaella Bernardi bernardi@inf.unibz.it P.zza Domenicani 3, Room 2.28 Faculty of Computer Science, Free University of Bolzano-Bozen http://www.inf.unibz.it/~bernardi/courses/logic06
More informationExamples: P: it is not the case that P. P Q: P or Q P Q: P implies Q (if P then Q) Typical formula:
Logic: The Big Picture Logic is a tool for formalizing reasoning. There are lots of different logics: probabilistic logic: for reasoning about probability temporal logic: for reasoning about time (and
More informationCOMP 2600: Formal Methods for Software Engineeing
COMP 2600: Formal Methods for Software Engineeing Dirk Pattinson Semester 2, 2013 What do we mean by FORMAL? Oxford Dictionary in accordance with convention or etiquette or denoting a style of writing
More informationMat 243 Exam 1 Review
OBJECTIVES (Review problems: on next page) 1.1 Distinguish between propositions and non-propositions. Know the truth tables (i.e., the definitions) of the logical operators,,,, and Write truth tables for
More information1.1 Language and Logic
c Oksana Shatalov, Fall 2017 1 1.1 Language and Logic Mathematical Statements DEFINITION 1. A proposition is any declarative sentence (i.e. it has both a subject and a verb) that is either true or false,
More informationLogic and Propositional Calculus
CHAPTER 4 Logic and Propositional Calculus 4.1 INTRODUCTION Many algorithms and proofs use logical expressions such as: IF p THEN q or If p 1 AND p 2, THEN q 1 OR q 2 Therefore it is necessary to know
More informationLecture 6: Finite Fields
CCS Discrete Math I Professor: Padraic Bartlett Lecture 6: Finite Fields Week 6 UCSB 2014 It ain t what they call you, it s what you answer to. W. C. Fields 1 Fields In the next two weeks, we re going
More informationLecture Notes on DISCRETE MATHEMATICS. Eusebius Doedel
Lecture Notes on DISCRETE MATHEMATICS Eusebius Doedel c Eusebius J. Doedel, 009 Contents Logic. Introduction............................................................................... Basic logical
More informationPredicate Logic. Andreas Klappenecker
Predicate Logic Andreas Klappenecker Predicates A function P from a set D to the set Prop of propositions is called a predicate. The set D is called the domain of P. Example Let D=Z be the set of integers.
More information2-1. Inductive Reasoning and Conjecture. Lesson 2-1. What You ll Learn. Active Vocabulary
2-1 Inductive Reasoning and Conjecture What You ll Learn Scan Lesson 2-1. List two headings you would use to make an outline of this lesson. 1. Active Vocabulary 2. New Vocabulary Fill in each blank with
More information2/2/2018. CS 103 Discrete Structures. Chapter 1. Propositional Logic. Chapter 1.1. Propositional Logic
CS 103 Discrete Structures Chapter 1 Propositional Logic Chapter 1.1 Propositional Logic 1 1.1 Propositional Logic Definition: A proposition :is a declarative sentence (that is, a sentence that declares
More informationCS103 Handout 09 Fall 2012 October 19, 2012 Problem Set 4
CS103 Handout 09 Fall 2012 October 19, 2012 Problem Set 4 This fourth problem set explores propositional and first-order logic, along with its applications. Once you've completed it, you should have a
More informationPREDICATE LOGIC. Schaum's outline chapter 4 Rosen chapter 1. September 11, ioc.pdf
PREDICATE LOGIC Schaum's outline chapter 4 Rosen chapter 1 September 11, 2018 margarita.spitsakova@ttu.ee ICY0001: Lecture 2 September 11, 2018 1 / 25 Contents 1 Predicates and quantiers 2 Logical equivalences
More informationLogic. Quantifiers. (real numbers understood). x [x is rotten in Denmark]. x<x+x 2 +1
Logic One reason for studying logic is that we need a better notation than ordinary English for expressing relationships among various assertions or hypothetical states of affairs. A solid grounding in
More informationSınav : FELSEFE (INGILIZCE-TÜRKÇE DILINDE)(G.O.Ö.D) Yarışma Sınavı. 5 "... is branch of philosophy and focus on
1 "Philosophy is focus on..." Choose the correct word ) Education B ) Law C ) Mind D ) Politics 5 "... is branch of philosophy and focus on knowledge." Choose the correct word ) Ethic B ) Logic C ) Ontology
More informationMATH 22 INFERENCE & QUANTIFICATION. Lecture F: 9/18/2003
MATH 22 Lecture F: 9/18/2003 INFERENCE & QUANTIFICATION Sixty men can do a piece of work sixty times as quickly as one man. One man can dig a post-hole in sixty seconds. Therefore, sixty men can dig a
More informationChapter 2: The Logic of Quantified Statements. January 22, 2010
Chapter 2: The Logic of Quantified Statements January 22, 2010 Outline 1 2.1- Introduction to Predicates and Quantified Statements I 2 2.2 - Introduction to Predicates and Quantified Statements II 3 2.3
More informationSupplementary Logic Notes CSE 321 Winter 2009
1 Propositional Logic Supplementary Logic Notes CSE 321 Winter 2009 1.1 More efficient truth table methods The method of using truth tables to prove facts about propositional formulas can be a very tedious
More informationCS 70 Discrete Mathematics and Probability Theory Fall 2016 Seshia and Walrand Midterm 1 Solutions
CS 70 Discrete Mathematics and Probability Theory Fall 2016 Seshia and Walrand Midterm 1 Solutions PRINT Your Name: Answer: Oski Bear SIGN Your Name: PRINT Your Student ID: CIRCLE your exam room: Dwinelle
More informationUniversity of Ottawa CSI 2101 Midterm Test Instructor: Lucia Moura. February 9, :30 pm Duration: 1:50 hs. Closed book, no calculators
University of Ottawa CSI 2101 Midterm Test Instructor: Lucia Moura February 9, 2010 11:30 pm Duration: 1:50 hs Closed book, no calculators Last name: First name: Student number: There are 5 questions and
More informationINTENSIONS MARCUS KRACHT
INTENSIONS MARCUS KRACHT 1. The Way Things Are This note accompanies the introduction of Chapter 4 of the lecture notes. I shall provide some formal background and technology. Let a language L be given
More informationQuantifiers. P. Danziger
- 2 Quantifiers P. Danziger 1 Elementary Quantifiers (2.1) We wish to be able to use variables, such as x or n in logical statements. We do this by using the two quantifiers: 1. - There Exists 2. - For
More informationGeneric Size Theory Gary Hardegree Department of Philosophy University of Massachusetts Amherst, MA 01003
Generic Size Theory Gary Hardegree Department of Philosophy University of Massachusetts Amherst, MA 01003 1. Introduction The Euclidian Paradigm...1 2. A Simple Example A Generic Theory of Size...1 1.
More informationA Guide to Proof-Writing
A Guide to Proof-Writing 437 A Guide to Proof-Writing by Ron Morash, University of Michigan Dearborn Toward the end of Section 1.5, the text states that there is no algorithm for proving theorems.... Such
More informationModal logics and their semantics
Modal logics and their semantics Joshua Sack Department of Mathematics and Statistics, California State University Long Beach California State University Dominguez Hills Feb 22, 2012 Relational structures
More informationPhilosophy 5340 Epistemology. Topic 3: Analysis, Analytically Basic Concepts, Direct Acquaintance, and Theoretical Terms. Part 2: Theoretical Terms
Philosophy 5340 Epistemology Topic 3: Analysis, Analytically Basic Concepts, Direct Acquaintance, and Theoretical Terms Part 2: Theoretical Terms 1. What Apparatus Is Available for Carrying out Analyses?
More informationFormal Logic. Critical Thinking
ormal Logic Critical hinking Recap: ormal Logic If I win the lottery, then I am poor. I win the lottery. Hence, I am poor. his argument has the following abstract structure or form: If P then Q. P. Hence,
More informationSolving Equations by Adding and Subtracting
SECTION 2.1 Solving Equations by Adding and Subtracting 2.1 OBJECTIVES 1. Determine whether a given number is a solution for an equation 2. Use the addition property to solve equations 3. Determine whether
More informationLetter to Hooke. Rubric Score Leuwenhoek Impersonation
Letter to Hooke There's 104 days of summer vacation, and school comes along just to end it. So the annual problem for your generation is finding a good way to spend it. So out of boredom one summer day,
More information1A Logic 2013 Model Answers
1A Logic 2013 Model Answers Section A 1. This is a question about TFL. Attempt all parts of this question. [Note that most of the material in this question has been moved to the metatheory section of the
More informationBound and Free Variables. Theorems and Proofs. More valid formulas involving quantifiers:
Bound and Free Variables More valid formulas involving quantifiers: xp(x) x P(x) Replacing P by P, we get: x P(x) x P(x) Therefore x P(x) xp(x) Similarly, we have xp(x) x P(x) x P(x) xp(x) i(i 2 > i) is
More informationDirect Proof and Counterexample I:Introduction
Direct Proof and Counterexample I:Introduction Copyright Cengage Learning. All rights reserved. Goal Importance of proof Building up logic thinking and reasoning reading/using definition interpreting :
More informationPhilosophy 240: Symbolic Logic
Philosophy 240: Symbolic Logic Russell Marcus Hamilton College Fall 2015 Class #41 - Second-Order Quantification Marcus, Symbolic Logic, Slide 1 Second-Order Inferences P Consider a red apple and a red
More informationAssignment 3 Logic and Reasoning KEY
Assignment 3 Logic and Reasoning KEY Print this sheet and fill in your answers. Please staple the sheets together. Turn in at the beginning of class on Friday, September 8. Recall this about logic: Suppose
More informationPropositional Language - Semantics
Propositional Language - Semantics Lila Kari University of Waterloo Propositional Language - Semantics CS245, Logic and Computation 1 / 41 Syntax and semantics Syntax Semantics analyzes Form analyzes Meaning
More information