Logic and Reasoning Practice Final Exam Spring Section Number
|
|
- James Chandler
- 7 years ago
- Views:
Transcription
1 Logic and Reasoning Practice Final Exam Spring 2015 Name Section Number The final examination is worth 100 points. 1. (5 points) What is an argument? Explain what is meant when one says that logic is the normative study of arguments. In what way(s) is the standard for assessing the goodness of an argument different for deductive and inductive arguments? 2. (5 points) Fill in the truth tables below, where (P % Q ) = ((P ~Q ) (~P Q )): P Q (P Q) (P Q) (P Q) (P % Q)
2 Do ONE of the following two problems. Only the first completed problem will be graded. 3. (5 points) Use truth tables to decide whether the argument below is valid or invalid. ((P ~Q ) Q ) (Q ~R ) ~R 4. (5 points) Use truth tables to classify the two sentences below (tautologous, selfcontradictory, or contingent) and then compare them by saying which and how many of the following categories apply: equivalent, contradictory, consistent, and inconsistent. ~(~(~(P ~Q ) ~P ) ~P ) ~(P P )
3 5. In the following problems, you are asked to prove some alternative rules of inference. a. (3 points) Addition { P } (P Q ) [3 lines] b. (4 points) Contraposition { (P Q ) } (~Q ~P ) [5 lines] c. (3 points) Disjunctive Syllogism { (P Q ), ~P } Q [11 lines]
4 6. (5 points) Translate the following argument into our zeroth-order formal language and then give a proof to show that the argument is valid. John is not allowed to argue unless Michael has paid. If John argues, then John is allowed to argue. John argues. Michael has paid.
5 7. (5 points) Suppose that Billy loves Suzy, Suzy loves Jane, and Jane loves only herself. Use a directed graph to represent the relation x loves y as it applies to Billy, Suzy, and Jane. Is the relation an equivalence relation? Justify your answer.
6 8. Answer the questions below about small worlds, models, and validity. For Parts (a) and (b), consider a small world consisting of three objects named a, b, and c such that for predicates F and G, all of the following are true: Fa, Fb, ~Fc, ~Ga, ~Gb, and Gc. a. (2 points) Is the small world a model for the sentence (( x)fx ( y)gy)? Explain your answer. b. (2 points) Is the small world a model for the sentence ( x)(fx Gx)? Explain your answer. c. (1 point) What, if anything, can you say about the logical relationship(s) between the sentences in Parts (a) and (b)? Explain your answer.
7 9. (5 points) For this problem, you may purchase up to two hints for one point per hint. Give a natural deduction proof [10 lines] to show the following: { } (( x)~dx ( y)dy)
8 10. (5 points) Translate the following argument into our formal language and then give a proof to show that the argument is valid. Given that the argument is valid, are you rationally compelled to believe that ethics is not worth studying? Explain your answer. Every principle in ethics has some counter-example. If so, then particularism is true. Ethics is worth studying only if particularism is not true. Ethics is not worth studying.
9 11. Answer the questions below about sets and set theory. a. (3 points) How many elements are in the set A = {x, y, {x, y, {w}}, z}? b. (3 points) If B is the set {x, w, {y}, z}, what is the intersection (A B) of A and B? c. (2 points) List all of the subsets of the set C = {α, β, λ}. d. (2 points) Explain why the empty set is a subset of every set.
10 12. Answer the questions about probability below by referring to the following diagram: a. (3 points) What is the probability that a randomly-chosen object is shaded? b. (3 points) What is the probability that a randomly-chosen object is an unshaded triangle? c. (2 points) What is the probability that a randomly-chosen object is either an unshaded triangle or a shaded circle? d. (2 points) What is the probability that a randomly-chosen object is a triangle given that it is shaded?
11 13. Answer the following conceptual questions about probability. a. (4 points) Suppose your friend Rudy says he thinks there is a 50 percent chance that a Democrat will be elected President in 2016 and that it is twice as likely that a Republican will be elected. Is Rudy s statement coherent? Explain your answer. b. (3 points) Rudy assigns probability 0.8 to the sentence ( x)fx. What probability should Rudy assign to the sentence ~( x)~fx? Explain your answer. c. (3 points) One day, Rudy tells you about a woman he met named Jane. Jane is a registered member of the Democratic Party and regularly contributes to a blog discussing gender bias in hiring practices. Rudy says that he thinks it is less likely that Jane is a bank teller than it is that Jane is a feminist and a bank teller. Is Rudy s claim reasonable or not? Explain your answer.
12 Do ONE of the following two problems. Only the first completed problem will be graded. 14. (5 points) John Connor is constantly on the run from terminator cyborgs. In his experience, about one person in a thousand is a terminator cyborg. John has noticed that terminators are much more likely than ordinary humans to say, Thank you for explaining, after receiving an answer to a question. His corresponding credences are 0.8 and 0.2. One day, John overhears someone nearby say, Thank you for explaining, what degree of belief should he have that the person he overheard is a terminator cyborg? 15. (5 points) Your doctor is a Bayesian who once took a very good logic course as an undergraduate. You go in to see her with a severe headache and a cough. She thinks there is a 75% chance that you only have tension headaches, a 20% chance that you have meningitis, and a 5% chance that you have something else. She collects a sample of cerebrospinal fluid and tests it using gram staining. If you do not have meningitis, the test will be negative with probability one. But even if you do have meningitis, the test has a 40% chance of coming back negative. Suppose the test comes back negative. What is the probability that you have meningitis?
13 16. (5 points) Compare and contrast the three interpretations of probability discussed in lecture. Do philosophical debates about how to interpret probability matter? If so, how? If not, why not?
14 17. (5 points) Suppose Talan has a box full of colored blocks. One in five of the blocks are red. If Talan pulls out seven blocks one at a time and puts each block back before pulling out another, what is the probability that he pulls out exactly four red blocks?
15 18. (5 points) Suppose you have two trick coins. One has a bias of 1/3 for heads, and the other has a bias of 2/3 for heads. You cannot tell them apart just by looking, and you have forgotten which one is which. So, you decide to flip one of them several times and make a guess at which it is. You flip the coin ten times and observe heads come up six times. Set up the formula that you need in order to calculate the probability that you have been flipping the coin that has a 1/3 probability of heads on any given flip. Do not calculate a numerical answer. How would your answer change if you had picked your coin out of a bag of 20 coins in which all but one had a bias of 1/3 for heads?
16 BONUS #1: The Drinker Paradox. (5 points) Give a natural deduction proof to show the following: { } ( x)(dx ( y)dy) You might find it helpful to use the result of Problem #9 in your proof. If Dx = x drinks at the Pig and Whistle, what does the sentence that you are being asked to prove say in English? Now that you have translated the sentence, does it seem plausible to you? If not, what do you think has gone wrong? Explain your answers.
17 BONUS #2: Bayesian Statistics. (5 points) Give a conceptual account of how a Bayesian makes inferences about the world. Illustrate with a data-generating process that might plausibly be modeled with a binomial distribution.
CHAPTER 3. Methods of Proofs. 1. Logical Arguments and Formal Proofs
CHAPTER 3 Methods of Proofs 1. Logical Arguments and Formal Proofs 1.1. Basic Terminology. An axiom is a statement that is given to be true. A rule of inference is a logical rule that is used to deduce
More informationInvalidity in Predicate Logic
Invalidity in Predicate Logic So far we ve got a method for establishing that a predicate logic argument is valid: do a derivation. But we ve got no method for establishing invalidity. In propositional
More informationPhilosophical argument
Michael Lacewing Philosophical argument At the heart of philosophy is philosophical argument. Arguments are different from assertions. Assertions are simply stated; arguments always involve giving reasons.
More informationSolving Equations. How do you know that x = 3 in the equation, 2x - 1 = 5?
Question: Solving Equations How do you know that x = 3 in the equation, 2x - 1 = 5? Possible answers to the question are: 1. If you use guess and check, the only number that works for x is 3. 2. Why should
More information6.3 Conditional Probability and Independence
222 CHAPTER 6. PROBABILITY 6.3 Conditional Probability and Independence Conditional Probability Two cubical dice each have a triangle painted on one side, a circle painted on two sides and a square painted
More informationVieta s Formulas and the Identity Theorem
Vieta s Formulas and the Identity Theorem This worksheet will work through the material from our class on 3/21/2013 with some examples that should help you with the homework The topic of our discussion
More informationAnswer Key for California State Standards: Algebra I
Algebra I: Symbolic reasoning and calculations with symbols are central in algebra. Through the study of algebra, a student develops an understanding of the symbolic language of mathematics and the sciences.
More informationHomework 3 (due Tuesday, October 13)
Homework (due Tuesday, October 1 Problem 1. Consider an experiment that consists of determining the type of job either blue-collar or white-collar and the political affiliation Republican, Democratic,
More informationA Few Basics of Probability
A Few Basics of Probability Philosophy 57 Spring, 2004 1 Introduction This handout distinguishes between inductive and deductive logic, and then introduces probability, a concept essential to the study
More informationComparison of frequentist and Bayesian inference. Class 20, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Comparison of frequentist and Bayesian inference. Class 20, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom 1 Learning Goals 1. Be able to explain the difference between the p-value and a posterior
More informationWriting learning objectives
Writing learning objectives This material was excerpted and adapted from the following web site: http://www.utexas.edu/academic/diia/assessment/iar/students/plan/objectives/ What is a learning objective?
More informationWOLLONGONG COLLEGE AUSTRALIA. Diploma in Information Technology
First Name: Family Name: Student Number: Class/Tutorial: WOLLONGONG COLLEGE AUSTRALIA A College of the University of Wollongong Diploma in Information Technology Final Examination Spring Session 2008 WUCT121
More information3. Mathematical Induction
3. MATHEMATICAL INDUCTION 83 3. Mathematical Induction 3.1. First Principle of Mathematical Induction. Let P (n) be a predicate with domain of discourse (over) the natural numbers N = {0, 1,,...}. If (1)
More informationSection 6.1 Discrete Random variables Probability Distribution
Section 6.1 Discrete Random variables Probability Distribution Definitions a) Random variable is a variable whose values are determined by chance. b) Discrete Probability distribution consists of the values
More informationHandout #1: Mathematical Reasoning
Math 101 Rumbos Spring 2010 1 Handout #1: Mathematical Reasoning 1 Propositional Logic A proposition is a mathematical statement that it is either true or false; that is, a statement whose certainty or
More informationConditional Probability, Independence and Bayes Theorem Class 3, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Conditional Probability, Independence and Bayes Theorem Class 3, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom 1 Learning Goals 1. Know the definitions of conditional probability and independence
More information3.6. The factor theorem
3.6. The factor theorem Example 1. At the right we have drawn the graph of the polynomial y = x 4 9x 3 + 8x 36x + 16. Your problem is to write the polynomial in factored form. Does the geometry of the
More informationUndergraduate Notes in Mathematics. Arkansas Tech University Department of Mathematics
Undergraduate Notes in Mathematics Arkansas Tech University Department of Mathematics An Introductory Single Variable Real Analysis: A Learning Approach through Problem Solving Marcel B. Finan c All Rights
More information3. Logical Reasoning in Mathematics
3. Logical Reasoning in Mathematics Many state standards emphasize the importance of reasoning. We agree disciplined mathematical reasoning is crucial to understanding and to properly using mathematics.
More informationINCIDENCE-BETWEENNESS GEOMETRY
INCIDENCE-BETWEENNESS GEOMETRY MATH 410, CSUSM. SPRING 2008. PROFESSOR AITKEN This document covers the geometry that can be developed with just the axioms related to incidence and betweenness. The full
More informationPredicate Logic Review
Predicate Logic Review UC Berkeley, Philosophy 142, Spring 2016 John MacFarlane 1 Grammar A term is an individual constant or a variable. An individual constant is a lowercase letter from the beginning
More informationProbability: Terminology and Examples Class 2, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom
Probability: Terminology and Examples Class 2, 18.05, Spring 2014 Jeremy Orloff and Jonathan Bloom 1 Learning Goals 1. Know the definitions of sample space, event and probability function. 2. Be able to
More informationProblem of the Month: Fair Games
Problem of the Month: The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:
More informationCurriculum Alignment Project
Curriculum Alignment Project Math Unit Date: Unit Details Title: Solving Linear Equations Level: Developmental Algebra Team Members: Michael Guy Mathematics, Queensborough Community College, CUNY Jonathan
More informationWhat happens when logic and psychology meet?
Logic meets psychology 1 What happens when logic and psychology meet? 27 September 2005 Core Logic Logic and Cognition Group m.e.counihan@uva.nl kamer 218 (Vendelstraat 8) tel. 020-525 4531 Logic meets
More informationMath 3000 Section 003 Intro to Abstract Math Homework 2
Math 3000 Section 003 Intro to Abstract Math Homework 2 Department of Mathematical and Statistical Sciences University of Colorado Denver, Spring 2012 Solutions (February 13, 2012) Please note that these
More informationMathematics for Computer Science/Software Engineering. Notes for the course MSM1F3 Dr. R. A. Wilson
Mathematics for Computer Science/Software Engineering Notes for the course MSM1F3 Dr. R. A. Wilson October 1996 Chapter 1 Logic Lecture no. 1. We introduce the concept of a proposition, which is a statement
More informationWhen Betting Odds and Credences Come Apart: More Worries for Dutch Book Arguments
When Betting Odds and Credences Come Apart: More Worries for Dutch Book Arguments Darren BRADLEY and Hannes LEITGEB If an agent believes that the probability of E being true is 1/2, should she accept a
More informationFive High Order Thinking Skills
Five High Order Introduction The high technology like computers and calculators has profoundly changed the world of mathematics education. It is not only what aspects of mathematics are essential for learning,
More informationLikewise, we have contradictions: formulas that can only be false, e.g. (p p).
CHAPTER 4. STATEMENT LOGIC 59 The rightmost column of this truth table contains instances of T and instances of F. Notice that there are no degrees of contingency. If both values are possible, the formula
More informationMathematical Induction
Mathematical Induction In logic, we often want to prove that every member of an infinite set has some feature. E.g., we would like to show: N 1 : is a number 1 : has the feature Φ ( x)(n 1 x! 1 x) How
More informationAssessment For The California Mathematics Standards Grade 6
Introduction: Summary of Goals GRADE SIX By the end of grade six, students have mastered the four arithmetic operations with whole numbers, positive fractions, positive decimals, and positive and negative
More informationMathematics Georgia Performance Standards
Mathematics Georgia Performance Standards K-12 Mathematics Introduction The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by
More informationMOST FREQUENTLY ASKED INTERVIEW QUESTIONS. 1. Why don t you tell me about yourself? 2. Why should I hire you?
MOST FREQUENTLY ASKED INTERVIEW QUESTIONS 1. Why don t you tell me about yourself? The interviewer does not want to know your life history! He or she wants you to tell how your background relates to doing
More informationG C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Performance Assessment Task Circle and Squares Grade 10 This task challenges a student to analyze characteristics of 2 dimensional shapes to develop mathematical arguments about geometric relationships.
More informationDescriptive Statistics and Measurement Scales
Descriptive Statistics 1 Descriptive Statistics and Measurement Scales Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample
More informationLecture 9 Maher on Inductive Probability
Lecture 9 Maher on Inductive Probability Patrick Maher Scientific Thought II Spring 2010 Two concepts of probability Example You know that a coin is either two-headed or two-tailed but you have no information
More informationLecture Note 1 Set and Probability Theory. MIT 14.30 Spring 2006 Herman Bennett
Lecture Note 1 Set and Probability Theory MIT 14.30 Spring 2006 Herman Bennett 1 Set Theory 1.1 Definitions and Theorems 1. Experiment: any action or process whose outcome is subject to uncertainty. 2.
More informationConditional Probability
6.042/18.062J Mathematics for Computer Science Srini Devadas and Eric Lehman April 21, 2005 Lecture Notes Conditional Probability Suppose that we pick a random person in the world. Everyone has an equal
More informationBrought to you by the NVCC-Annandale Reading and Writing Center
Brought to you by the NVCC-Annandale Reading and Writing Center WORKSHOP OBJECTIVES: To understand the steps involved in writing inclass essays To be able to decode the question so that you answer the
More informationBeyond Propositional Logic Lukasiewicz s System
Beyond Propositional Logic Lukasiewicz s System Consider the following set of truth tables: 1 0 0 1 # # 1 0 # 1 1 0 # 0 0 0 0 # # 0 # 1 0 # 1 1 1 1 0 1 0 # # 1 # # 1 0 # 1 1 0 # 0 1 1 1 # 1 # 1 Brandon
More informationFirst Affirmative Speaker Template 1
First Affirmative Speaker Template 1 upon the gender of the Chairman.) DEFINITION 2A. We define the topic as (Explain what the topic means. Define the key or important words in the topic. Use a dictionary
More information6th Grade Lesson Plan: Probably Probability
6th Grade Lesson Plan: Probably Probability Overview This series of lessons was designed to meet the needs of gifted children for extension beyond the standard curriculum with the greatest ease of use
More informationWriting Thesis Defense Papers
Writing Thesis Defense Papers The point of these papers is for you to explain and defend a thesis of your own critically analyzing the reasoning offered in support of a claim made by one of the philosophers
More informationNF5-12 Flexibility with Equivalent Fractions and Pages 110 112
NF5- Flexibility with Equivalent Fractions and Pages 0 Lowest Terms STANDARDS preparation for 5.NF.A., 5.NF.A. Goals Students will equivalent fractions using division and reduce fractions to lowest terms.
More informationLecture 17 : Equivalence and Order Relations DRAFT
CS/Math 240: Introduction to Discrete Mathematics 3/31/2011 Lecture 17 : Equivalence and Order Relations Instructor: Dieter van Melkebeek Scribe: Dalibor Zelený DRAFT Last lecture we introduced the notion
More informationProblem of the Month Through the Grapevine
The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards: Make sense of problems
More informationMathematics. What to expect Resources Study Strategies Helpful Preparation Tips Problem Solving Strategies and Hints Test taking strategies
Mathematics Before reading this section, make sure you have read the appropriate description of the mathematics section test (computerized or paper) to understand what is expected of you in the mathematics
More informationPractice with Proofs
Practice with Proofs October 6, 2014 Recall the following Definition 0.1. A function f is increasing if for every x, y in the domain of f, x < y = f(x) < f(y) 1. Prove that h(x) = x 3 is increasing, using
More informationBBC Learning English Funky Phrasals Dating
BBC Learning English Funky Phrasals Dating Grammar auction You are going to buy correct sentences. First, read the sentences below and decide whether they are correct or incorrect. Decide what your maximum
More informationReview for Test 2. Chapters 4, 5 and 6
Review for Test 2 Chapters 4, 5 and 6 1. You roll a fair six-sided die. Find the probability of each event: a. Event A: rolling a 3 1/6 b. Event B: rolling a 7 0 c. Event C: rolling a number less than
More information1.2 Forms and Validity
1.2 Forms and Validity Deductive Logic is the study of methods for determining whether or not an argument is valid. In this section we identify some famous valid argument forms. Argument Forms Consider
More informationStatistics 100A Homework 7 Solutions
Chapter 6 Statistics A Homework 7 Solutions Ryan Rosario. A television store owner figures that 45 percent of the customers entering his store will purchase an ordinary television set, 5 percent will purchase
More informationFor example, estimate the population of the United States as 3 times 10⁸ and the
CCSS: Mathematics The Number System CCSS: Grade 8 8.NS.A. Know that there are numbers that are not rational, and approximate them by rational numbers. 8.NS.A.1. Understand informally that every number
More informationLesson 1. Basics of Probability. Principles of Mathematics 12: Explained! www.math12.com 314
Lesson 1 Basics of Probability www.math12.com 314 Sample Spaces: Probability Lesson 1 Part I: Basic Elements of Probability Consider the following situation: A six sided die is rolled The sample space
More informationChapter 3. Cartesian Products and Relations. 3.1 Cartesian Products
Chapter 3 Cartesian Products and Relations The material in this chapter is the first real encounter with abstraction. Relations are very general thing they are a special type of subset. After introducing
More informationThe fundamental question in economics is 2. Consumer Preferences
A Theory of Consumer Behavior Preliminaries 1. Introduction The fundamental question in economics is 2. Consumer Preferences Given limited resources, how are goods and service allocated? 1 3. Indifference
More informationTwo Fundamental Theorems about the Definite Integral
Two Fundamental Theorems about the Definite Integral These lecture notes develop the theorem Stewart calls The Fundamental Theorem of Calculus in section 5.3. The approach I use is slightly different than
More informationActivity 1: Using base ten blocks to model operations on decimals
Rational Numbers 9: Decimal Form of Rational Numbers Objectives To use base ten blocks to model operations on decimal numbers To review the algorithms for addition, subtraction, multiplication and division
More informationStatistics 2014 Scoring Guidelines
AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home
More informationProblem of the Month: Perfect Pair
Problem of the Month: The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:
More informationPredicate logic Proofs Artificial intelligence. Predicate logic. SET07106 Mathematics for Software Engineering
Predicate logic SET07106 Mathematics for Software Engineering School of Computing Edinburgh Napier University Module Leader: Uta Priss 2010 Copyright Edinburgh Napier University Predicate logic Slide 1/24
More information(LMCS, p. 317) V.1. First Order Logic. This is the most powerful, most expressive logic that we will examine.
(LMCS, p. 317) V.1 First Order Logic This is the most powerful, most expressive logic that we will examine. Our version of first-order logic will use the following symbols: variables connectives (,,,,
More informationKant s deontological ethics
Michael Lacewing Kant s deontological ethics DEONTOLOGY Deontologists believe that morality is a matter of duty. We have moral duties to do things which it is right to do and moral duties not to do things
More informationProbability. a number between 0 and 1 that indicates how likely it is that a specific event or set of events will occur.
Probability Probability Simple experiment Sample space Sample point, or elementary event Event, or event class Mutually exclusive outcomes Independent events a number between 0 and 1 that indicates how
More informationP1. All of the students will understand validity P2. You are one of the students -------------------- C. You will understand validity
Validity Philosophy 130 O Rourke I. The Data A. Here are examples of arguments that are valid: P1. If I am in my office, my lights are on P2. I am in my office C. My lights are on P1. He is either in class
More informationTHE BANACH CONTRACTION PRINCIPLE. Contents
THE BANACH CONTRACTION PRINCIPLE ALEX PONIECKI Abstract. This paper will study contractions of metric spaces. To do this, we will mainly use tools from topology. We will give some examples of contractions,
More information2.1. Inductive Reasoning EXAMPLE A
CONDENSED LESSON 2.1 Inductive Reasoning In this lesson you will Learn how inductive reasoning is used in science and mathematics Use inductive reasoning to make conjectures about sequences of numbers
More informationFull and Complete Binary Trees
Full and Complete Binary Trees Binary Tree Theorems 1 Here are two important types of binary trees. Note that the definitions, while similar, are logically independent. Definition: a binary tree T is full
More informationBook Review of Rosenhouse, The Monty Hall Problem. Leslie Burkholder 1
Book Review of Rosenhouse, The Monty Hall Problem Leslie Burkholder 1 The Monty Hall Problem, Jason Rosenhouse, New York, Oxford University Press, 2009, xii, 195 pp, US $24.95, ISBN 978-0-19-5#6789-8 (Source
More informationCONSTRUCTING A LOGICAL ARGUMENT
Sloan Communication Program Teaching Note CONSTRUCTING A LOGICAL ARGUMENT The purpose of most business writing is to recommend some course of action ("we should open a branch office in Duluth"; "management
More informationCartesian Products and Relations
Cartesian Products and Relations Definition (Cartesian product) If A and B are sets, the Cartesian product of A and B is the set A B = {(a, b) :(a A) and (b B)}. The following points are worth special
More informationLogic Appendix. Section 1 Truth Tables CONJUNCTION EXAMPLE 1
Logic Appendix T F F T Section 1 Truth Tables Recall that a statement is a group of words or symbols that can be classified collectively as true or false. The claim 5 7 12 is a true statement, whereas
More informationMATHEMATICS: REPEATING AND GROWING PATTERNS First Grade. Kelsey McMahan. Winter 2012 Creative Learning Experiences
MATHEMATICS: REPEATING AND GROWING PATTERNS Kelsey McMahan Winter 2012 Creative Learning Experiences Without the arts, education is ineffective. Students learn more and remember it longer when they are
More informationComparing Simple and Compound Interest
Comparing Simple and Compound Interest GRADE 11 In this lesson, students compare various savings and investment vehicles by calculating simple and compound interest. Prerequisite knowledge: Students should
More informationCONCEPTUAL CONTINGENCY AND ABSTRACT EXISTENCE
87 CONCEPTUAL CONTINGENCY AND ABSTRACT EXISTENCE BY MARK COLYVAN Mathematical statements such as There are infinitely many prime numbers and 2 ℵ 0 > ℵ 0 are usually thought to be necessarily true. Not
More informationLecture 2: Moral Reasoning & Evaluating Ethical Theories
Lecture 2: Moral Reasoning & Evaluating Ethical Theories I. Introduction In this ethics course, we are going to avoid divine command theory and various appeals to authority and put our trust in critical
More information6.2 Permutations continued
6.2 Permutations continued Theorem A permutation on a finite set A is either a cycle or can be expressed as a product (composition of disjoint cycles. Proof is by (strong induction on the number, r, of
More informationPART A: For each worker, determine that worker's marginal product of labor.
ECON 3310 Homework #4 - Solutions 1: Suppose the following indicates how many units of output y you can produce per hour with different levels of labor input (given your current factory capacity): PART
More informationCritical Analysis So what does that REALLY mean?
Critical Analysis So what does that REALLY mean? 1 The words critically analyse can cause panic in students when they first turn over their examination paper or are handed their assignment questions. Why?
More informationA Short Course in Logic Example 8
A Short ourse in Logic xample 8 I) Recognizing Arguments III) valuating Arguments II) Analyzing Arguments valuating Arguments with More than one Line of Reasoning valuating If then Premises Independent
More informationProblem of the Month: Cutting a Cube
Problem of the Month: The Problems of the Month (POM) are used in a variety of ways to promote problem solving and to foster the first standard of mathematical practice from the Common Core State Standards:
More informationSection 6.1 Joint Distribution Functions
Section 6.1 Joint Distribution Functions We often care about more than one random variable at a time. DEFINITION: For any two random variables X and Y the joint cumulative probability distribution function
More informationsome ideas on essays and essay writing
Disability and Dyslexia Service: Study Skills for Students some ideas on essays and essay writing why this document might be helpful for students: Before beginning work on an essay, it is vital to know
More informationOpen-Ended Problem-Solving Projections
MATHEMATICS Open-Ended Problem-Solving Projections Organized by TEKS Categories TEKSING TOWARD STAAR 2014 GRADE 7 PROJECTION MASTERS for PROBLEM-SOLVING OVERVIEW The Projection Masters for Problem-Solving
More informationHoover High School Math League. Counting and Probability
Hoover High School Math League Counting and Probability Problems. At a sandwich shop there are 2 kinds of bread, 5 kinds of cold cuts, 3 kinds of cheese, and 2 kinds of dressing. How many different sandwiches
More informationUmmmm! Definitely interested. She took the pen and pad out of my hand and constructed a third one for herself:
Sum of Cubes Jo was supposed to be studying for her grade 12 physics test, but her soul was wandering. Show me something fun, she said. Well I wasn t sure just what she had in mind, but it happened that
More informationGeometry Chapter 2 Study Guide
Geometry Chapter 2 Study Guide Short Answer ( 2 Points Each) 1. (1 point) Name the Property of Equality that justifies the statement: If g = h, then. 2. (1 point) Name the Property of Congruence that justifies
More informationVocabulary. Term Page Definition Clarifying Example. biconditional statement. conclusion. conditional statement. conjecture.
CHAPTER Vocabulary The table contains important vocabulary terms from Chapter. As you work through the chapter, fill in the page number, definition, and a clarifying example. biconditional statement conclusion
More informationOne natural response would be to cite evidence of past mornings, and give something like the following argument:
Hume on induction Suppose you were asked to give your reasons for believing that the sun will come up tomorrow, in the form of an argument for the claim that the sun will come up tomorrow. One natural
More informationHow To Understand The Relation Between Simplicity And Probability In Computer Science
Chapter 6 Computation 6.1 Introduction In the last two chapters we saw that both the logical and the cognitive models of scientific discovery include a condition to prefer simple or minimal explanations.
More informationHOW TO WRITE A THEOLOGICAL PAPER 1 Begin everything with prayer!!! 1. Choice of the Topic. 2. Relevant Scriptural Texts
HOW TO WRITE A THEOLOGICAL PAPER 1 Begin everything with prayer!!! 1 st Step: Choose a Topic and Relevant Scriptural Texts 1. Choice of the Topic Criteria Edification Manageability Detail Choose a topic
More informationInductive Reasoning Page 1 of 7. Inductive Reasoning
Inductive Reasoning Page 1 of 7 Inductive Reasoning We learned that valid deductive thinking begins with at least one universal premise and leads to a conclusion that is believed to be contained in the
More informationThat s Not Fair! ASSESSMENT #HSMA20. Benchmark Grades: 9-12
That s Not Fair! ASSESSMENT # Benchmark Grades: 9-12 Summary: Students consider the difference between fair and unfair games, using probability to analyze games. The probability will be used to find ways
More informationMetric Spaces. Chapter 1
Chapter 1 Metric Spaces Many of the arguments you have seen in several variable calculus are almost identical to the corresponding arguments in one variable calculus, especially arguments concerning convergence
More informationLecture 8 The Subjective Theory of Betting on Theories
Lecture 8 The Subjective Theory of Betting on Theories Patrick Maher Philosophy 517 Spring 2007 Introduction The subjective theory of probability holds that the laws of probability are laws that rational
More informationIs a monetary incentive a feasible solution to some of the UK s most pressing health concerns?
Norwich Economics Papers June 2010 Is a monetary incentive a feasible solution to some of the UK s most pressing health concerns? ALEX HAINES A monetary incentive is not always the key to all of life's
More informationKant s Fundamental Principles of the Metaphysic of Morals
Kant s Fundamental Principles of the Metaphysic of Morals G. J. Mattey Winter, 2015/ Philosophy 1 The Division of Philosophical Labor Kant generally endorses the ancient Greek division of philosophy into
More informationE3: PROBABILITY AND STATISTICS lecture notes
E3: PROBABILITY AND STATISTICS lecture notes 2 Contents 1 PROBABILITY THEORY 7 1.1 Experiments and random events............................ 7 1.2 Certain event. Impossible event............................
More informationSyllogisms and Fallacies 101
1 Syllogisms and Fallacies 101 This isn t a course in logic, but all educated people should know the basic vocabulary and the basic underlying logic of the syllogism. Major premise: No reptiles have fur.
More information