Relation: A relation is simply a set of ordered pairs.
|
|
- Joshua Willis
- 6 years ago
- Views:
Transcription
1 Relations: UNIT 5: FUNCTIONS STUDY SHEET Relation: A relation is simply a set o ordered pairs. The irst elements in the ordered pairs (the -values), orm the domain. The second elements in the ordered pairs (the y-values), orm the rane. Only the elements "used" by the relation constitute the rane. This mappin shows a relation rom set A into set B. This relation consists o the ordered pairs (1,2), (3,2), (5,7), and (9,8). The domain is the set {1, 3, 5, 9}. The rane is the set {2, 7, 8}. (Notice that 3, 5 and 6 are not part o the rane.) The rane is the dependent variable. The ollowin are eamples o relations. Notice that a vertical line may intersect a relation in more than one location. This set o 5 points is a relation. {(1,2), (2, 4), (3, 5), (2, 6), (1, -3)} Notice that vertical lines may intersect more than one point at a time. This parabola is also a relation. Notice that a vertical line can intersect this raph twice.
2 Functions: I we impose the ollowin rule on a relation, it becomes a unction. Function: A unction is a set o ordered pairs in which each -element has only ONE y-element associated with it. The relations shown above are NOT unctions because certain - elements are paired with more than one unique y-element. The irst relation shown above can be altered to become a unction by removin the ordered pairs where the -coordinate is repeated. It will not matter which "repeat" is removed. unction: {(1,2), (2,4), (3,5)} The raph at the riht shows that a vertical line now intersects only ONE point in our new unction. Vertical line test: each vertical line drawn throuh the raph will intersect a unction in only one location.
3 Functional Notation: Traditionally, unctions are reerred to by the letter name, but need not be the only letter used in unction names. The ollowin are but a ew o the notations that may be used to name a unction: (), (), h(a), A(t),... Note: The () notation can be thouht o as another way o representin the y-value in a unction, especially when raphin. The y-ais is even labeled as the () ais, when raphin. Evaluatin Functions: To evaluate a unction, simply replace (substitute) the unction's variable with the indicated number or epression. 1. A unction is represented by () = Find (3). 2. To ind (3), replace the -value with 3. (3) = 2(3) + 5 = 11. The answer, 11, is called the imae o 3 under (). To ind (3h+2), replace the -values with 3h + 2. Usin parentheses or this substitution will help prevent alebraic errors. Use (3h + 2) when substitutin.
4 Domain and Rane: The domain is the set o all irst elements o ordered pairs (-coordinates). The rane is the set o all second elements o ordered pairs (y-coordinates). Domain and rane can be seen clearly rom a raph. Eample 1: Eample 2: Domain: {1, 3, 4, 6} Rane: {-2, 2, 5} Domain: Rane: (all real numbers)
5 Composition o Functions: The term "composition o unctions" (or "composite unction") reers to the combinin o unctions in a manner where the output rom one unction becomes the input or the net unction. In math terms, the rane (the y-value answers) o one unction becomes the domain (the -values) o the net unction. The notation used or composition is: and is read " composed with o " or " o o ". Notice how the letters stay in the same order in each epression or the composition. (()) clearly tells you to start with unction (innermost parentheses are done irst). Composition o unctions can be thouht o as a series o taicab rides or your values. The eample below shows unctions and workin toether to create the composition. Note: The startin domain or unction is bein limited to the our values 1, 2, 3 and 4 or this eample. Eamples: Now, suppose that we wish to write our composition as an alebraic epression. 1. Substitute the epression or unction (in this case 2) or () in the composition. This will clearly show you the order o the substitutions that will need to be made. 2. Now, substitute this epression (2) into unction in place o the -value. Perorm any needed simpliications (none needed in this eample). 1. Given the unctions and, ind a.) and b.) Answer: a.) b.) Notice that and do not necessarily yield the same answer. Composition o unctions is not commutative.
6 2. Given the unctions and, ind a.) and b.) Answer: a.) = h(p(3)) where p(3) ives an answer o 5 and h(5) then ives an answer o 25. The answer is 25. b.) One-to-One Function: A unction rom A to B is called one-to-one (or 1-1) i whenever (a) = (b) then a = b. No element o B is the imae o more than one element in A. In a one-to-one unction, iven any y there is only one that can be paired with the iven y. "One-to-One" NOT "One-to-One"
7 INVERSE FUNCTIONS: Basically speakin, the process o indin an inverse is simply the swappin o the and y coordinates. This newly ormed inverse will be a relation, but may not necessarily be a unction. Consider this subtle dierence in terminoloy: Deinition: INVERSE OF A FUNCTION: The relation ormed when the independent variable is echaned with the dependent variable in a iven relation. (This inverse may NOT be a unction.) Remember: The inverse o a unction may not always be a unction! The oriinal unction must be a one-to-one unction to uarantee that its inverse will also be a unction. Deinition: A unction is a one-to-one unction i and only i each second element corresponds to one and only one irst element. (each and y value is used only once) Use the horizontal line test to determine i a unction is a one-to-one unction. I ANY horizontal line intersects your oriinal unction in ONLY ONE location, your unction will be a one-to-one unction and its inverse will also be a unction. The unction y = 3 + 2, shown at the riht, IS a one-to-one unction and its inverse will also be a unction. (Remember that the vertical line test is used to show that a relation is a unction.) Deinition: The inverse o a unction is the set o ordered pairs obtained by interchanin the irst and second elements o each pair in the oriinal unction. Should the inverse o unction () also be a unction, this inverse unction is denoted by -1 (). Note: I the oriinal unction is a one-to-one unction, the inverse will be a unction. [The notation -1 () reers to "inverse unction". It does not alebraically mean 1/ ().] I a unction is composed with its inverse unction, the result is the startin value. Think o it as the unction and the inverse undoin one another when composed. Consider the simple unction () = {(1,2), (3,4), (5,6)} and its inverse -1 () = {(2,1), (4,3), (6,5)}
8 "So, how do we ind inverses?" Consider the ollowin methods: Swap ordered pairs: I your unction is deined as a list o ordered pairs, simply swap the and y values. Remember, the inverse relation will be a unction only i the oriinal unction is one-to-one. Eamples: a. Given unction, ind the inverse relation. Is the inverse relation also a unction? Answer: Function is a one-to-one unction since the and y values are used only once. Since unction is a oneto-one unction, the inverse relation is also a unction. Thereore, the inverse unction is: b. Determine the inverse o this unction. Is the inverse also a unction? () Answer: Swap the and y variables to create the inverse relation. The inverse relation will be the set o ordered pairs: {(2,1), (0,-2), (3,-1), (-1,0), (1,2), (-2,3), (5,4),(1,-3)} Since unction was not a one-to-one unction (the y value o 1 was used twice), the inverse relation will NOT be a unction (because the value o 1 now ets mapped to two separate y values which is not possible or unctions).
9 Solve alebraically: Solvin or an inverse relation alebraically is a three step process: Eamples: a. Find the inverse o the unction Answer: Remember: Set = y. Swap the variables. Solve or y. 1. Set the unction = y 2. Swap the and y variables 3. Solve or y Use the inverse unction notation since () is a one-to-one unction. b. Find the inverse o the unction (iven that is not equal to 0). Answer: Remember: Set = y. Swap the variables. Eliminate the raction by multiplyin each side by y. Get the y's on one side o the equal sin by subtractin y rom each side. Isolate the y by actorin out the y. Solve or y. Use the inverse unction notation since () is a one-to-one unction.
10 Deinitions o operations o unctions: Sum Dierence Product Quotient 0 ) ( ; Composition ) (
11 Averae Rate o Chane:
12
Unit 5: Inverse Functions
Haberman MTH Section I: Functions and Their Graphs Unit 5: Inverse Functions EXAMPLE: Consider the unction n( ), which is graphed in Figure Figure : Graph o n( ) Since n is a unction, each input corresponds
More informationModule 6: Inverse Functions
Haberman MTH c Section I: Sets and Functions Module 6: Inverse Functions EXAMPLE: Consider the unction n ( ), which is graphed in Figure below Figure : Graph o n( ) Since n is a unction, each input corresponds
More informationFUNCTIONS OF ONE REAL VARIABLE
FUNCTIONS OF ONE REAL VARIABLE Concept o a unction Real unction o one real variable is a mapping rom the set M, a subset in real numbers R, to the set o all real numbers R. Function is a rule, by which
More informationFunctions and Function Notation
SECTION P Functions and Their Graphs 9 Section P X Domain Range = () Y A real-valued unction o a real variable Figure P Functions and Their Graphs Use unction notation to represent and evaluate a unction
More information2.5 Inverse Functions
. Invere unction What i an Invere unction? An invere unction i a unction that undoe another unction. A an eample the unction add the number to the variable. onequentl, an invere unction uch a g that ubtract
More information1. Show that f is a bijective
3 Functions 4 SECTION C Inverse Functions B the end o this section ou will be able to show that a given unction is bijective ind the inverse unction You need to know our work on injections and surjections
More informationAlgebraic, Exponential, and Logarithmic Functions
Alebraic, Eponential, and Loarithmic Functions Chapter : Functions and Mathematical Models Chapter : Properties o Elementar Functions Chapter : Fittin Functions to Data Chapter : Polnomial and Rational
More informationFinal Review Ch. 1 #1
Final Review Ch. 1 #1 9th Grade Algebra 1A / Algebra 1 Beta (Ms. Dalton) Student Name/ID: Instructor Note: Show all of your work! 1. Translate the phrase into an algebraic expression. more than 2. Translate
More informationFinal Exam (PRACTICE-2) #2
Final Exam (PRACTICE-2) #2 Basic Math / FND M020 FA 14 10404-10N30FD04-Nap (Prof. Abdon) Student Name/ID: 1. Estimate by first rounding each number to the nearest hundred. 2. Give the digits in the thousands
More informationGeorgia Quality Core Curriculum
correlated to the Grade 8 Georgia Quality Core Curriculum McDougal Littell 3/2000 Objective (Cite Numbers) M.8.1 Component Strand/Course Content Standard All Strands: Problem Solving; Algebra; Computation
More informationMcDougal Littell High School Math Program. correlated to. Oregon Mathematics Grade-Level Standards
Math Program correlated to Grade-Level ( in regular (non-capitalized) font are eligible for inclusion on Oregon Statewide Assessment) CCG: NUMBERS - Understand numbers, ways of representing numbers, relationships
More informationMidterm Review. Intermediate Algebra / MAT135 S2014 test (Mr. Porter)
Midterm Review Intermediate Algebra / MAT135 S2014 test (Mr. Porter) Student Name/ID: 1. Solve for. 2. Solve for. 3. At the city museum, child admission is and adult admission is. On Wednesday, tickets
More informationMidterm Review Part 1 #4
Midterm Review Part 1 #4 Intermediate Algebra / MAT135 S2014 sec 042 (Prof. Fleischner) Student Name/ID: 1. Solve for. 2. Solve for. 3. A Web music store offers two versions of a popular song. The size
More informationShort-Circuits on FPGAs caused by Partial Runtime Reconfiguration
2010 International Conerence on Field Prorammable Loic and Applications Short-Circuits on FPGAs caused by Partial Runtime Reconiuration Christian Beckho Email: christian@recobus.de Dirk Koch and Jim Torresen
More informationFinal Exam (PRACTICE-3) #3
Final Exam (PRACTICE-3) #3 Basic Math / FND M020 FA 14 10404-10N30FD04-Nap (Prof. Abdon) Student Name/ID: 1. Dale went to a store and bought items. Each item cost How much did he spend? 2. Estimate by
More informationMLLunsford, Spring Activity: Conditional Probability and The Law of Total Probability
MLLunsford, Spring 2003 1 Activity: Conditional Probability and The Law of Total Probability Concepts: Conditional Probability, Independent Events, the Multiplication Rule, the Law of Total Probability
More informationA House Divided: GIS Exercise
Name: Date: A House Divided: GIS Exercise It is 1947 and you have been selected to serve on the United Nations Ad Hoc Committee on the Palestinian Question. Palestine has been administered as a British
More informationEdexcel GCSE Religious Studies
Resources Guide Edexcel GCSE Reliious Studies Presentin our own resources for the new 2009 GCSE specification Great Support: Better results Edexcel GCSE Reliious Studies Presentin our own resources for
More informationDigital Logic Lecture 5 Boolean Algebra and Logic Gates Part I
Digital Logic Lecture 5 Boolean Algebra and Logic Gates Part I By Ghada Al-Mashaqbeh The Hashemite University Computer Engineering Department Outline Introduction. Boolean variables and truth tables. Fundamental
More informationOrder your FREE Evaluation Pack. Edexcel GCSE Religious Studies. Order your FREE Evaluation Pack. Want to know more?
Order your FREE Evaluation Pack Our GCSE Reliious Studies Evaluation Pack includes Unit 1A: Reliion and Life Christianity and Islam Student Book and accompanyin support material. Simply complete and return
More informationArtificial Intelligence Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras
(Refer Slide Time: 00:26) Artificial Intelligence Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras Lecture - 06 State Space Search Intro So, today
More informationGrade 6 Math Connects Suggested Course Outline for Schooling at Home
Grade 6 Math Connects Suggested Course Outline for Schooling at Home I. Introduction: (1 day) Look at p. 1 in the textbook with your child and learn how to use the math book effectively. DO: Scavenger
More informationScriptures and Doctrine :: question about Jesus' name
question about Jesus' name - posted by anonymity, on: 2010/6/13 13:50 First, how do you pronounce it in Hebrew? Yeshua Hamashiach? Or Yehoshua or what? Second, It means God's chosen savior basically riht?
More informationMath Matters: Why Do I Need To Know This? 1 Logic Understanding the English language
Math Matters: Why Do I Need To Know This? Bruce Kessler, Department of Mathematics Western Kentucky University Episode Two 1 Logic Understanding the English language Objective: To introduce the concept
More information1. Introduction Formal deductive logic Overview
1. Introduction 1.1. Formal deductive logic 1.1.0. Overview In this course we will study reasoning, but we will study only certain aspects of reasoning and study them only from one perspective. The special
More informationCurriculum Guide for Pre-Algebra
Unit 1: Variable, Expressions, & Integers 2 Weeks PA: 1, 2, 3, 9 Where did Math originate? Why is Math possible? What should we expect as we use Math? How should we use Math? What is the purpose of using
More informationArtificial Intelligence: Valid Arguments and Proof Systems. Prof. Deepak Khemani. Department of Computer Science and Engineering
Artificial Intelligence: Valid Arguments and Proof Systems Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras Module 02 Lecture - 03 So in the last
More informationSEVENTH GRADE RELIGION
SEVENTH GRADE RELIGION will learn nature, origin and role of the sacraments in the life of the church. will learn to appreciate and enter more fully into the sacramental life of the church. THE CREED ~
More informationHP-35s Calculator Program Eccentrically Loaded Connections
Program for HP35s Calculator Page 1 HP-35s Calculator Program Eccentrically Loaded Connections Author: J. E. Charalambides Date: August 18/2012 2012 J. E. Charalambides Line Instruction Process User Instruction
More information2.1 Review. 2.2 Inference and justifications
Applied Logic Lecture 2: Evidence Semantics for Intuitionistic Propositional Logic Formal logic and evidence CS 4860 Fall 2012 Tuesday, August 28, 2012 2.1 Review The purpose of logic is to make reasoning
More informationKey Stage: 2 Year: Lower Juniors Subject: Being a Sikh Time allocation: 1 hour per week
Key Stae: 2 Year: Lower Juniors Subject: Bein a Time allocation: 1 hour per week Part Learnin Objectives Activities and Experiences Key Questions 1 To learn about the namin ceremony. meanins of names.
More informationSemantic Entailment and Natural Deduction
Semantic Entailment and Natural Deduction Alice Gao Lecture 6, September 26, 2017 Entailment 1/55 Learning goals Semantic entailment Define semantic entailment. Explain subtleties of semantic entailment.
More informationMath 11 Final Exam Review Part 3 #1
Math 11 Final Exam Review Part 3 #1 College Algebra / Math 11 RCC Fall 2011 #48794 (Prof. Chiek) Student Name/ID: 1. For each point in the table below, decide whether it is on Line 1, Line 2, both, or
More informationHoughton Mifflin MATHEMATICS
2002 for Mathematics Assessment NUMBER/COMPUTATION Concepts Students will describe properties of, give examples of, and apply to real-world or mathematical situations: MA-E-1.1.1 Whole numbers (0 to 100,000,000),
More informationRevisiting the Socrates Example
Section 1.6 Section Summary Valid Arguments Inference Rules for Propositional Logic Using Rules of Inference to Build Arguments Rules of Inference for Quantified Statements Building Arguments for Quantified
More informationII RESEMBLANCE NOMINALISM, CONJUNCTIONS
Meeting of the Aristotelian Society held at Senate House, University of London, on 22 October 2012 at 5:30 p.m. II RESEMBLANCE NOMINALISM, CONJUNCTIONS AND TRUTHMAKERS The resemblance nominalist says that
More informationRead this carefully before beginning the assessment!
SPIRITUAL GIFTS ASSESSMENT As followers of Jesus, God has given each of us specific spiritual gifts to use in the church for the purpose of accomplishing His mission in the world. This spiritual gifts
More informationReview for Test III #1
Review for Test III #1 Intermediate Algebra / MAT135 Spring 2010 (Prof Greenbaun) 1 Multiply Simplify your answer as much as possible 2 A car travels at an average speed of miles per hour How long does
More informationNow consider a verb - like is pretty. Does this also stand for something?
Kripkenstein The rule-following paradox is a paradox about how it is possible for us to mean anything by the words of our language. More precisely, it is an argument which seems to show that it is impossible
More informationLesson Objectives. Core Content Objectives. Language Arts Objectives. Core Vocabulary
The Louisiana Purchase 4 Lesson Objectives Core Content Objectives Students will: Locate the Mississippi River on a map Locate the Rocky Mountains on a map Identify and locate the Louisiana Territory on
More informationSpiritual Gifts Test
Spiritual Gifts Test God has blessed each believer with Spiritual Gifts. Do you know what Spiritual Gifts God has given you? This Spiritual Gifts Test will help you determine what Spiritual Gift(s) and/or
More informationBased on the translation by E. M. Edghill, with minor emendations by Daniel Kolak.
On Interpretation By Aristotle Based on the translation by E. M. Edghill, with minor emendations by Daniel Kolak. First we must define the terms 'noun' and 'verb', then the terms 'denial' and 'affirmation',
More informationHere s a very dumbed down way to understand why Gödel is no threat at all to A.I..
Comments on Godel by Faustus from the Philosophy Forum Here s a very dumbed down way to understand why Gödel is no threat at all to A.I.. All Gödel shows is that try as you might, you can t create any
More informationFinal Exam (PRACTICE-1) #1
Final Exam (PRACTICE-1) #1 Basic Math / FND M020 FA 14 10404-10N30FD04-Nap (Prof. Abdon) Student Name/ID: 1. There are basketball fans who plan to go to a game. How many buses will be needed, given that
More informationOn Interpretation. Section 1. Aristotle Translated by E. M. Edghill. Part 1
On Interpretation Aristotle Translated by E. M. Edghill Section 1 Part 1 First we must define the terms noun and verb, then the terms denial and affirmation, then proposition and sentence. Spoken words
More informationRosen, Discrete Mathematics and Its Applications, 6th edition Extra Examples
Rosen, Discrete Mathematics and Its Applications, 6th edition Extra Examples Section 1.1 Propositional Logic Page references correspond to locations of Extra Examples icons in the textbook. p.2, icon at
More informationYEAR: UNIT-SPECIFIC GOALS (italicized) Assessable Student Outcome
What s in the Bible? GRACEWAYS CONCEPT: GOD HELPS PEOPLE BY THE WORD YEAR: SUGGESTED DURATION: 5 weeks (approximately 135 minutes per week) DATE OF USE: FAITH STATEMENTS: 1 2 3 UPPER ELEMENTARY BAND Level
More informationAthanasius: On the Incarnation of the Word. Ernest W. Durbin II
Athanasius: On the Incarnation of the Word by Ernest W. Durbin II The Life and Thought of the Christian Church: Beginnings to about 1500 A.D. HCUS 5010 Walter Froese, Ph.D. November 1, 2004 1 ON THE INCARNATION
More informationNPTEL NPTEL ONINE CERTIFICATION COURSE. Introduction to Machine Learning. Lecture-59 Ensemble Methods- Bagging,Committee Machines and Stacking
NPTEL NPTEL ONINE CERTIFICATION COURSE Introduction to Machine Learning Lecture-59 Ensemble Methods- Bagging,Committee Machines and Stacking Prof. Balaraman Ravindran Computer Science and Engineering Indian
More information15. Russell on definite descriptions
15. Russell on definite descriptions Martín Abreu Zavaleta July 30, 2015 Russell was another top logician and philosopher of his time. Like Frege, Russell got interested in denotational expressions as
More informationSome observations on identity, sameness and comparison
Some observations on identity, sameness and comparison Line Mikkelsen Meaning Sciences Club, UC Berkeley, October 16, 2012 1 Introduction The meaning of the English adjective same is in one sense obvious:
More informationTitle of Unit Plan: A Study of St. Patrick
Name of Teacher: Shelly Kraus Title of Unit Plan: A Study of St. Patrick Subject Area: Language Arts Grade Level: Third Grade Estimated Duration of Unit: Two Weeks Cross Curricular Opportunities: Religion,
More informationAbility, Schooling Inputs and Earnings: Evidence from the NELS
Ability, Schooling Inputs and Earnings: Evidence from the NELS Ozkan Eren University of Nevada, Las Vegas June 2008 Introduction I The earnings dispersion among individuals for a given age, education level,
More informationDiscipleship Self-Evaluation Assessment!
Discipleship Self-Evaluation Assessment! This task is a self-test to see where you are now as a follower of Jesus. There is no right or wrong answer to these questions. Your answer to each question is
More informationAffirmation-Negation: New Perspective
Journal of Modern Education Review, ISSN 2155-7993, USA November 2014, Volume 4, No. 11, pp. 910 914 Doi: 10.15341/jmer(2155-7993)/11.04.2014/005 Academic Star Publishing Company, 2014 http://www.academicstar.us
More informationAccommodations: How will I accommodate individual needs of students? See Lesson 1 for ideas. Supplies:
Lesson 8: Achan Sins Objectives: Students will 1) Understand the severe consequences that can occur when we sin 2) Understand that sometimes when someone sins even others have to pay the consequence 3)
More informationABSTRACT. Religion and Economic Growth: An Analysis at the City Level. Ran Duan, M.S.Eco. Mentor: Lourenço S. Paz, Ph.D.
ABSTRACT Religion and Economic Growth: An Analysis at the City Level Ran Duan, M.S.Eco. Mentor: Lourenço S. Paz, Ph.D. This paper looks at the effect of religious beliefs on economic growth using a Brazilian
More informationThe Question, the Answer & the Promise Psalm 15
The Question, the Answer & the Promise Psalm 15 1 O Lord, who shall sojourn in your tent? Who shall dwell on your holy hill? 2 He who walks blamelessly and does what is right and speaks truth in his heart;
More informationKnights of Columbus-Marist Poll January 2011
How to Read Banners Banners are a simple way to display tabular data. The following provides an explanation of how to read the banners. 1. Thinking of the entire table as a grid of cells, each cell contains
More informationPDM2005_G3_SL1-36_01-18_F 06/15/ :03 PM Page 1 Student Pages 1
Student Pages 1 Name 21 Party Time It is April 2 and Emily is walking to school. She is thinking about her birthday party, which will be on April 30. When she looked at the calendar that morning, she saw
More informationTHIRD GRADE CURRICULUM RELIGION
THIRD GRADE CURRICULUM RELIGION Creed: Demonstrate an understanding of the human need for God based on revelation and faith Understand that God takes care of us and is always faithful to us Recognize the
More informationLesson 09 Notes. Machine Learning. Intro
Machine Learning Lesson 09 Notes Intro C: Hi Michael. M: Hey how's it going? C: So I want to talk about something today Michael. I want to talk about Bayesian Learning, and I've been inspired by our last
More informationWhole Numbers_Mid-Term Exam Review #1
Whole Numbers_Mid-Term Exam Review #1 Basic Math / FND M010 FA 14 10398-10N20FD04-Nap (Prof. Abdon) Student Name/ID: 1. Give the digits in the thousands place and the hundreds place. thousands: hundreds:
More informationTHE SEVEN-FOLD STRUCTURE OF CHRISTIANITY
Page-1 THE SEVEN-FOLD STRUCTURE OF CHRISTIANITY April 14 th, 2004 John H. Painter TABLE OF CONTENTS. THE SEVEN-FOLD STRUCTURE OF CHRISTIANITY... 1 TABLE OF CONTENTS... 1 INTRODUCTION.... 1 Romans-12 Gifts
More informationHP-35s Calculator Program Triangle Solution (Program Based on Sine & Cosine Rules)
Program for HP35s Calculator Page 1 HP-35s Calculator Program Triangle Solution (Program Based on Sine & Cosine Rules) 2016 Date: May 1/2016 Line Instruction Process User Instruction T001 LBL T Establishing
More informationTranscription ICANN Los Angeles Translation and Transliteration Contact Information PDP WG Update to the Council meeting Saturday 11 October 2014
Transcription ICANN Los Angeles Translation and Transliteration Contact Information PDP WG Update to the Council meeting Saturday 11 October 2014 Note: The following is the output of transcribing from
More informationThe way we convince people is generally to refer to sufficiently many things that they already know are correct.
Theorem A Theorem is a valid deduction. One of the key activities in higher mathematics is identifying whether or not a deduction is actually a theorem and then trying to convince other people that you
More informationLogic: The Science that Evaluates Arguments
Logic: The Science that Evaluates Arguments Logic teaches us to develop a system of methods and principles to use as criteria for evaluating the arguments of others to guide us in constructing arguments
More informationArtificial Intelligence Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras
(Refer Slide Time: 00:14) Artificial Intelligence Prof. Deepak Khemani Department of Computer Science and Engineering Indian Institute of Technology, Madras Lecture - 35 Goal Stack Planning Sussman's Anomaly
More informationRamsey s belief > action > truth theory.
Ramsey s belief > action > truth theory. Monika Gruber University of Vienna 11.06.2016 Monika Gruber (University of Vienna) Ramsey s belief > action > truth theory. 11.06.2016 1 / 30 1 Truth and Probability
More informationLower Key Stage 2 Two Year Rolling Programme
Year One Year Two Term Autumn Spring Summer Autumn Spring Summer Theme The Romans Scotl/Wales Keeping Healthy Famous People The Rainforest Ancient Greece National Curriculum Subject English Please refer
More information(1) A phrase may be denoting, and yet not denote anything; e.g., 'the present King of France'.
On Denoting By Russell Based on the 1903 article By a 'denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the
More informationILLUSTRATIVE MATERIAL
KAPPELER INSTITUTE RECORDINGS ILLUSTRATIVE MATERIAL DIVINE CYBERNETICS: THE PROTO-SCIENCE, THE INTEGRAL SCIENCE (Tape code: D-2) Max Kappeler 1969, 2005 Kappeler Institute for the Science of Being All
More informationMAKING RIGHT DECISIONS
MAKING RIGHT DECISIONS Strong Families, Great Churches In the spiritual world, those who want to live Godly lives are always being persecuted. When the church changes and rises in the spirit world, nations
More informationReliabilism: Holistic or Simple?
Reliabilism: Holistic or Simple? Jeff Dunn jeffreydunn@depauw.edu 1 Introduction A standard statement of Reliabilism about justification goes something like this: Simple (Process) Reliabilism: S s believing
More informationThe Need For Authority
The Need For Authority Mt. 21:23-27 The Need For Authority Why Ask This Question Among The Lord s People? Preachers In Lord s Church Don t Understand Basis Every Departure From Truth Misunderstanding Of
More informationANGELS SPECIALIST SCHOOL INTERNATIONAL SCHEME OF WORK FOR MATHEMATICS (TERM 2) GRADE 3
ANGELS SPECIALIST SCHOOL INTERNATIONAL SCHEME OF WORK FOR MATHEMATICS (TERM 2) GRADE 3 Week Topics Objectives 1&2. Review - Use the = sign to represent equality e.g. 75+25=95+5 Multiplication and Division
More information1.2. What is said: propositions
1.2. What is said: propositions 1.2.0. Overview In 1.1.5, we saw the close relation between two properties of a deductive inference: (i) it is a transition from premises to conclusion that is free of any
More informationCS 2104 Intro Problem Solving in Computer Science Test 1 READ THIS NOW!
READ THIS NOW! Print your name in the space provided below. There are 5 problems, priced as marked. The maximum score is 100. The grading of each question will take into account whether you obtained a
More informationGenesis 1:1-13 King James Version September 2, 2018
Genesis 1:1-13 King James Version September 2, 2018 The International Bible Lesson (Uniform Sunday School Lessons Series) for Sunday, September 2, 2018, is from Genesis 1:1-13. Questions for Discussion
More information6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 Transcript Lecture 3
6.041SC Probabilistic Systems Analysis and Applied Probability, Fall 2013 Transcript Lecture 3 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare
More informationOur Strategy Where is God taking Us? Week 3 September 23, 2018
Our Strategy Where is God taking Us? Week 3 September 23, 2018 LEARNING GOALS Ø Realize the need to offer clear steps for individuals to take. Ø Understand the biblical context for taking steps to grow
More informationContextual two-dimensionalism
Contextual two-dimensionalism phil 93507 Jeff Speaks November 30, 2009 1 Two two-dimensionalist system of The Conscious Mind.............. 1 1.1 Primary and secondary intensions...................... 2
More informationUtilitas 14(2): , Conditional and Conditioned Reasons. David McNaughton and Piers Rawling
1 Utilitas 14(2): 240-248, 2002 Conditional and Conditioned Reasons David McNaughton and Piers Rawling In his interesting and helpful paper 'McNaughton and Rawling on the Agentrelative/Agent-neutral Distinction,'
More informationCircularity in ethotic structures
Synthese (2013) 190:3185 3207 DOI 10.1007/s11229-012-0135-6 Circularity in ethotic structures Katarzyna Budzynska Received: 28 August 2011 / Accepted: 6 June 2012 / Published online: 24 June 2012 The Author(s)
More informationPreview Party. Christmas Fair. Round Hill Community Church The News Letter December Christmas on Round Hill PASTOR S MESSAGE.
PASTOR S MESSAGE Round Hill Community Church The News Letter December 2012 Christmas wasn t always celebrated the way it is today. In the days ollowin the Protestant Reormation in the 16th century, December
More informationPublished in Analysis 61:1, January Rea on Universalism. Matthew McGrath
Published in Analysis 61:1, January 2001 Rea on Universalism Matthew McGrath Universalism is the thesis that, for any (material) things at any time, there is something they compose at that time. In McGrath
More informationGenesis 1:1-13 English Standard Version September 2, 2018
Genesis 1:1-13 English Standard Version September 2, 2018 The International Bible Lesson (Uniform Sunday School Lessons Series) for Sunday, September 2, 2018, is from Genesis 1:1-13. Questions for Discussion
More informationLearning About World Religions: Buddhism
Learning About World Religions: Buddhism I N T E R A C T I V E S T U D E N T N O T E B O O K What are the main beliefs and teachings of Buddhism? P R E V I E W What is happiness? How do you achieve happiness?
More informationCovenant Christian Academy Handbook Table of Contents
1 Covenant Christian Academy Handbook Table of Contents Mission Statement. 2 Statement of Faith. 2-3 History and Purpose.. 3 Center Philosophy. 3-4 Goals for the Family. 4 Membership fees.. 4 Orientation
More information4.1 A problem with semantic demonstrations of validity
4. Proofs 4.1 A problem with semantic demonstrations of validity Given that we can test an argument for validity, it might seem that we have a fully developed system to study arguments. However, there
More informationWho Is The Greatest? Matthew 18:1-5
Lesson 242 Who Is The Greatest? Matthew 18:1-5 MEMORY VERSE MATTHEW 18:3... Assuredly, I say to you, unless you are c onv erted and bec om e as little c hildren, you w ill by no m eans enter the kingdom
More informationTRANSFORMING THE ORDINARY
BiSci3 1 of 1 Background and Context TRANSFORMING THE ORDINARY If you are a poet, you will see clearly that there is a cloud floating in this sheet of paper. Without a cloud, there will be no rain; without
More informationChapter 8 - Sentential Truth Tables and Argument Forms
Logic: A Brief Introduction Ronald L. Hall Stetson University Chapter 8 - Sentential ruth ables and Argument orms 8.1 Introduction he truth-value of a given truth-functional compound proposition depends
More informationA Discussion on Kaplan s and Frege s Theories of Demonstratives
Volume III (2016) A Discussion on Kaplan s and Frege s Theories of Demonstratives Ronald Heisser Massachusetts Institute of Technology Abstract In this paper I claim that Kaplan s argument of the Fregean
More informationSERMON THE LORD S PRAYER: HALLOWED BE YOUR NAME! MATTHEW 5:43-48 SUNDAY, 5 JUNE, 2016, 10 A.M. KEMNAY PARISH CHURCH
SERMON THE LORD S PRAYER: HALLOWED BE YOUR NAME! MATTHEW 5:43-48 SUNDAY, 5 JUNE, 2016, 10 A.M. KEMNAY PARISH CHURCH Let us pray: Our Father in Heaven, thank you for the words of Jesus Christ, which leads
More informationReviews WITTGENSTEIN, CRITIC OF RUSSELL. Russell Wahl. English and Philosophy / Idaho State U Pocatello, id 83209, usa
Reviews WITTGENSTEIN, CRITIC OF RUSSELL Russell Wahl English and Philosophy / Idaho State U Pocatello, id 83209, usa wahlruss@isu.edu Jérôme Sackur. Formes et faits: Analyse et théorie de la connaissance
More informationNPTEL NPTEL ONLINE COURSES REINFORCEMENT LEARNING. UCB1 Explanation (UCB1)
NPTEL NPTEL ONLINE COURSES REINFORCEMENT LEARNING UCB1 Explanation (UCB1) Prof. Balaraman Ravindran Department of Computer Science and Engineering Indian Institute of Technology Madras So we are looking
More informationNELSON MOTIVATIONAL SPIRITUAL GIFTS INVENTORY
NELSON MOIVAIONAL SPIRIUAL GIS INVENORY Instructions: his questionnaire is designed to help you discover your motivational spiritual gift referred to in Romans 12:4-8. Because this is computer scored,
More informationMOREY, JAMES MARSH ( ) PAPERS
State of Tennessee Department of State Tennessee State Library and Archives 403 Seventh Avenue North Nashville, Tennessee 37243-0312 MOREY, JAMES MARSH (1844-1923) PAPERS 1861-1942 Processed by: Marilyn
More information