1 On General Statements Being True or False

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "1 On General Statements Being True or False"

Transcription

1 MGF 1106: Exam 1 Supplementary Assignment 1 On General Statements Being True or False On the exam, you were given some true/false questions involving general statements in set theory. Before stating the new problems, we will begin by taking a look at how such true/false questions work in general, including a look at a few of the problems that appeared on the exam (or similar). Question: Is the following statement true or false? The sky is blue. Solution: You wake up tomorrow to find the following in your inbox: Dear Earthling, I am a bizarre alien from a distant planet called Glorbus 9. I used my telepathic tail to divine your address. All my friends here on Glorbus are jerks and I m headed to Earth for some time away. I m in a weird mood and I want to see something pretty. If I don t I will be very upset. Tell me, is the Earth sky blue? That is my favorite color. If you advise me well on this, I will grant you any wish you desire upon my arrival. (However, if you mislead me, I will swap your fingers and toes in anger!) Sincerely, Xeebfavv Zizwazz What do you reply? Of course, you might say, Yo, Xeebfavv, take it from me, this sky is blue. You re gonna love it! P.S. I want a Ferrari!... But, what if Xeebfavv shows up on a cloudy day? Or at sunset? Or at night?! If he sees a sky that isn t blue, you ll have to start endorsing your checks with your feet, which will be very embarrassing at the bank. Your best bet may be to reply, I m sorry Mr. Hope that helps. Zizwazz, no, the sky isn t always blue. Indeed, The sky is blue. is FALSE as a general statement, because it s not always true. 1

2 Question: Is the following statement true or false? A A B Solution: This, of course, was the first problem on the exam. written in words as follows: The statement may be For any two sets A and B, the union A B always contains A. In the form of an abstract Venn diagram, the statement claims the following: Hopefully the picture helps make this obvious; indeed, this general statement about unions is TRUE. By definition, the union of any set A and any set B is the set consisting of any and all elements which can be found in either A or B. Thus, all the elements in A also appear in the union A B, so A A B. We can test this by defining two sets A and B, however we want. For example, let A = {1, 3, 5, 6, 9} B = {2, 3, 6, 8} The union of these two sets is A B = {1, 2, 3, 5, 6, 8, 9} and, indeed, A = {1, 3, 5, 6, 9} {1, 2, 3, 5, 6, 8, 9} = A B 2

3 Question: Is the following statement true or false? A A B Solution: This is similar to the second problem on the exam. written in words as follows: The statement may be For any two sets A and B, the intersection A B always contains A. In the form of a Venn diagram, the statement claims that: Again, I hope the picture helps you conclude that this statement is FALSE. It is actually true for some choices of A and B (see below), but it is not true for all choices of A and B, so it is not true as a general statement. To give a concrete example of how this may fail, let: A = {1, 2, 3} B = {3, 4, 5} The intersection is A B = {3}, so A A B. Again, because the statement fails in at least one case, it is false as a general statement. Note, however, that this statement is actually true for some choices of A and B. example, letting For A = {1, 2, 3} B = {1, 2, 3, 4, 5} In this case, A B = A, so, yes, A A B. (Another for this to work is to let A =. Then A is a subset of any set!) 3

4 2 Shaded Area Problems Example: (from lecture) Express the shaded area using,, and/or. Solution: The shaded area is A, plus that extra little chunk outside of A. To add to a set, we can use unions. Note, however, that writing down what that little chunk is will be annoying. A better way to see this is as A, plus B C. A already includes some of B C, but there s no harm in throwing it in again, and writing this is much easier; So the shaded area is given by (parentheses are critical!) A (B C) 4

5 Example: Express the shaded area using,, and/or. Solution: Here, the area is B, minus the pacman mouth. A convenient way to delete portions of a set is to intersect with a compliment. But, again, the pacman mouth is not convenient to work with. The best way to see this area is that is everything in B: which is not in A C: So... 5

6 ... again, in words, the shaded area is: everything which is in B and not in A C; So, the shaded area is given by B (A C) Do- (You can also see this by shading (A C) and intersecting (overlapping) with B. ing this would be good practice!) 6

7 Name: MGF 1106: Exam 1 Supplementary Assignment 1. (10 points) Say whether each statement is true or false. In addition, if it is true, give an example to illustrate. If it is false, give an example where the statement fails. a) A A B b) A B B c) A B A B d) A C B C e) If A B, then A A B. 2. (10 points) Express each shaded area using,, and/or. (see next page for hints) 7

8 Hints for Problem 1: Remember, a statement like A A B is TRUE only if it is true for every two sets A and B. If you can find any particular pair of sets A and B for which it fails, the statement is FALSE. a) What if B A? b) Draw the statement as a Venn diagram (as in examples above). c) Careful, note that it is, not just. What if A B = A B? d) Draw a Venn diagram. e) If A B, then what is A B =? Hints for Problem 2: a) View as the union of two pieces; one piece is easy, the other was on the exam. b) View as two pieces (which may overlap). c) View as three pieces. d) View as two pieces. e) One piece is easy, ignoring that one, how do you get the other? 8

+ Section 6.2 and 6.3

+ Section 6.2 and 6.3 Section 6.2 and 6.3 Learning Objectives After this section, you should be able to DEFINE and APPLY basic rules of probability CONSTRUCT Venn diagrams and DETERMINE probabilities DETERMINE probabilities

More information

Set Theory: Shading Venn Diagrams

Set Theory: Shading Venn Diagrams Set Theory: Shading Venn Diagrams Venn diagrams are representations of sets that use pictures. We will work with Venn diagrams involving two sets (two-circle diagrams) and three sets (three-circle diagrams).

More information

OA3-10 Patterns in Addition Tables

OA3-10 Patterns in Addition Tables OA3-10 Patterns in Addition Tables Pages 60 63 Standards: 3.OA.D.9 Goals: Students will identify and describe various patterns in addition tables. Prior Knowledge Required: Can add two numbers within 20

More information

Applications of Methods of Proof

Applications of Methods of Proof CHAPTER 4 Applications of Methods of Proof 1. Set Operations 1.1. Set Operations. The set-theoretic operations, intersection, union, and complementation, defined in Chapter 1.1 Introduction to Sets are

More information

Statistical Inference. Prof. Kate Calder. If the coin is fair (chance of heads = chance of tails) then

Statistical Inference. Prof. Kate Calder. If the coin is fair (chance of heads = chance of tails) then Probability Statistical Inference Question: How often would this method give the correct answer if I used it many times? Answer: Use laws of probability. 1 Example: Tossing a coin If the coin is fair (chance

More information

God is Eternal Lesson 1

God is Eternal Lesson 1 Preschool Curriculum (4K / 5K) August 15 th & 16 th, 2009 God is Eternal Lesson 1 Divine Attribute: Heart Response: God is Eternal Be Amazed Memory Verse: Jesus Christ is the same yesterday, today and

More information

Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern.

Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern. INTEGERS Integers are positive and negative whole numbers, that is they are; {... 3, 2, 1,0,1,2,3...}. The dots mean they continue in that pattern. Like all number sets, integers were invented to describe

More information

Commander Seamoor of the Intergalactic Water Safety Patrol

Commander Seamoor of the Intergalactic Water Safety Patrol Commander Seamoor of the Intergalactic Water Safety Patrol Ranger: Hello girls and boys. Thank you for inviting me to your school. My name is Ranger. I am a Park Ranger with the U.S. Army Corps of Engineers.

More information

Basic concepts in probability. Sue Gordon

Basic concepts in probability. Sue Gordon Mathematics Learning Centre Basic concepts in probability Sue Gordon c 2005 University of Sydney Mathematics Learning Centre, University of Sydney 1 1 Set Notation You may omit this section if you are

More information

Study Success Formula

Study Success Formula Study Success Formula By: A. Adam This book may be distributed freely as long as the content is not altered or changed in anyway. Enjoy! Feel Free To Visit: www.study-habits.com/blog We are Open 24 hours

More information

What is a set? Sets. Specifying a Set. Notes. The Universal Set. Specifying a Set 10/29/13

What is a set? Sets. Specifying a Set. Notes. The Universal Set. Specifying a Set 10/29/13 What is a set? Sets CS 231 Dianna Xu set is a group of objects People: {lice, ob, Clara} Colors of a rainbow: {red, orange, yellow, green, blue, purple} States in the S: {labama, laska, Virginia, } ll

More information

NF5-12 Flexibility with Equivalent Fractions and Pages 110 112

NF5-12 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 information

[This page is designed for duplication as Transparency #1.]

[This page is designed for duplication as Transparency #1.] [This page is designed for duplication as Transparency #1.] The following problems require you to add or subtract fractions. Remember, the denominators (bottom numbers) must be the same, and they don t

More information

Probability OPRE 6301

Probability OPRE 6301 Probability OPRE 6301 Random Experiment... Recall that our eventual goal in this course is to go from the random sample to the population. The theory that allows for this transition is the theory of probability.

More information

(Refer Slide Time: 2:03)

(Refer Slide Time: 2:03) Control Engineering Prof. Madan Gopal Department of Electrical Engineering Indian Institute of Technology, Delhi Lecture - 11 Models of Industrial Control Devices and Systems (Contd.) Last time we were

More information

Aim To help students prepare for the Academic Reading component of the IELTS exam.

Aim To help students prepare for the Academic Reading component of the IELTS exam. IELTS Reading Test 1 Teacher s notes Written by Sam McCarter Aim To help students prepare for the Academic Reading component of the IELTS exam. Objectives To help students to: Practise doing an academic

More information

I look forward to doing business with you and hope we get the chance to meet soon

I look forward to doing business with you and hope we get the chance to meet soon Emailing 1: Worksheet 1 - Reading Tasks Dear Mr Smith, I would like to introduce myself. My name is Saarland and I am the new South Western sales manager for Chou Cream English Schools. The previous sales

More information

Exam Preparation and Memory Strategies

Exam Preparation and Memory Strategies Counselling & Learning Support North Vancouver Campus Student Success Workshops Exam Preparation and Memory Strategies BR 267 604.984.1744 www.capilanou.ca/services Prepared by: Alison Parry, Learning

More information

FOREIGN MATTER MANAGEMENT 36 QUESTION ASSESSMENT

FOREIGN MATTER MANAGEMENT 36 QUESTION ASSESSMENT Name: Employee I.D. or Personal I.D. Number: Company Name: Department: Head of Department: I understand that this 36 question test proves that I know what I am doing and therefore gives me no reason whatsoever

More information

Dance of Earth and Moon

Dance of Earth and Moon Science Benchmark: 03 : 01 Earth orbits around the sun, and the moon orbits around Earth. Earth is spherical in shape and rotates on its axis to produce the night and day cycle. To people on Earth, this

More information

GRADE 4 FLORIDA. Multiplication WORKSHEETS

GRADE 4 FLORIDA. Multiplication WORKSHEETS GRADE 4 FLORIDA Multiplication WORKSHEETS Multiplication facts 5 and 0 times tables The 5 and 0 times tables are easier if you learn them together. Answer the 5 times table: Count in 5s down the ladders:

More information

CmSc 175 Discrete Mathematics Lesson 10: SETS A B, A B

CmSc 175 Discrete Mathematics Lesson 10: SETS A B, A B CmSc 175 Discrete Mathematics Lesson 10: SETS Sets: finite, infinite, : empty set, U : universal set Describing a set: Enumeration = {a, b, c} Predicates = {x P(x)} Recursive definition, e.g. sequences

More information

Sets and set operations

Sets and set operations CS 441 Discrete Mathematics for CS Lecture 7 Sets and set operations Milos Hauskrecht milos@cs.pitt.edu 5329 Sennott Square asic discrete structures Discrete math = study of the discrete structures used

More information

2.1 Symbols and Terminology

2.1 Symbols and Terminology 2.1 Symbols and Terminology Definitions: set is a collection of objects. The objects belonging to the set are called elements, ormembers, oftheset. Sets can be designated in one of three different ways:

More information

A MIDDLE SCHOOL LESSON FOR CREATING AND USING DICHOTOMOUS KEYS By Sharon Donovan

A MIDDLE SCHOOL LESSON FOR CREATING AND USING DICHOTOMOUS KEYS By Sharon Donovan A MIDDLE SCHOOL LESSON FOR CREATING AND USING DICHOTOMOUS KEYS By Sharon Donovan INTRODUCTION One of my most enjoyable lessons is on the concept of dichotomous keys. It not only addresses a multitude of

More information

No Solution Equations Let s look at the following equation: 2 +3=2 +7

No Solution Equations Let s look at the following equation: 2 +3=2 +7 5.4 Solving Equations with Infinite or No Solutions So far we have looked at equations where there is exactly one solution. It is possible to have more than solution in other types of equations that are

More information

NO LONGER THE FIRST 2010 Josh Danz

NO LONGER THE FIRST 2010 Josh Danz NO LONGER THE FIRST 2010 Josh Danz Free performance of this play for high school and college level competitive forensics is permitted. All other rights reserved. The Intriguing Interp Series is published

More information

BBC LEARNING ENGLISH 6 Minute Vocabulary Reporting verbs

BBC LEARNING ENGLISH 6 Minute Vocabulary Reporting verbs BBC LEARNING ENGLISH 6 Minute Vocabulary Reporting verbs This is not a word-for-word transcript Hello! Welcome to 6 Minute Vocabulary with me, and me,. In this programme, we re looking at reporting verbs.

More information

Dr. Paul Haggan Barbara Larsen Jeff Minn

Dr. Paul Haggan Barbara Larsen Jeff Minn Dr. Paul Haggan Barbara Larsen Jeff Minn Choice and freedom to make mistakes. Adult demonstrates empathy and compassion. Child takes responsibility of his/her actions. Child learns from the consequences

More information

Section 1.5 Exponents, Square Roots, and the Order of Operations

Section 1.5 Exponents, Square Roots, and the Order of Operations Section 1.5 Exponents, Square Roots, and the Order of Operations Objectives In this section, you will learn to: To successfully complete this section, you need to understand: Identify perfect squares.

More information

Math/Stats 425 Introduction to Probability. 1. Uncertainty and the axioms of probability

Math/Stats 425 Introduction to Probability. 1. Uncertainty and the axioms of probability Math/Stats 425 Introduction to Probability 1. Uncertainty and the axioms of probability Processes in the real world are random if outcomes cannot be predicted with certainty. Example: coin tossing, stock

More information

CV and EV- Examples 1

CV and EV- Examples 1 CV and EV- Examples 1 Before we do any examples, let s make sure we have CV and EV straight. They re similar, but not the exact same thing, and which is which can get confusing. Both deal with changes

More information

1.4 Compound Inequalities

1.4 Compound Inequalities Section 1.4 Compound Inequalities 53 1.4 Compound Inequalities This section discusses a technique that is used to solve compound inequalities, which is a phrase that usually refers to a pair of inequalities

More information

Midterm exam PS 30 November 2005

Midterm exam PS 30 November 2005 Midterm exam PS 30 November 2005 Name: TA: Section number: This is a closed book exam. The only thing you can take into this exam is yourself and writing instruments. Everything you write should be your

More information

Let s talk today about creating your seating chart!

Let s talk today about creating your seating chart! Let s talk today about creating your seating chart! This is something that s done in the final weeks leading up to the wedding, and can be a big pain. I was thinking about why it s such a hassle, and I

More information

Lesson 22: Solution Sets to Simultaneous Equations

Lesson 22: Solution Sets to Simultaneous Equations Student Outcomes Students identify solutions to simultaneous equations or inequalities; they solve systems of linear equations and inequalities either algebraically or graphically. Classwork Opening Exercise

More information

Induction. Margaret M. Fleck. 10 October These notes cover mathematical induction and recursive definition

Induction. Margaret M. Fleck. 10 October These notes cover mathematical induction and recursive definition Induction Margaret M. Fleck 10 October 011 These notes cover mathematical induction and recursive definition 1 Introduction to induction At the start of the term, we saw the following formula for computing

More information

MAT 1000. Mathematics in Today's World

MAT 1000. Mathematics in Today's World MAT 1000 Mathematics in Today's World We talked about Cryptography Last Time We will talk about probability. Today There are four rules that govern probabilities. One good way to analyze simple probabilities

More information

2011-2012 PRESCHOOL WORSHIP SONGS

2011-2012 PRESCHOOL WORSHIP SONGS 2011-2012 PRESCHOOL WORSHIP SONGS ALL MY HEART I wanna love you, God With all my heart With all my heart I wanna love you, God with all my heart (whistling) I wanna love you, God Like Jesus did Like Jesus

More information

[child s full name] who arrived on [child s birth date]

[child s full name] who arrived on [child s birth date] This book was custom made for [child s full name] who arrived on [child s birth date] [dedication] [name book given from] [year book given] The day you were born was a dream come true. It began the lifetime

More information

TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers

TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime

More information

Check Skills You ll Need. New Vocabulary union intersection disjoint sets. Union of Sets

Check Skills You ll Need. New Vocabulary union intersection disjoint sets. Union of Sets NY-4 nion and Intersection of Sets Learning Standards for Mathematics..31 Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets). Check Skills You ll Need

More information

Another Helper (John 14:12-31)

Another Helper (John 14:12-31) 1 Another Helper (John 14:12-31) If you love me, you will keep my commands. And I will ask the father, and he will give you another helper, to be with you forever. This other helper is the spirit of truth.

More information

) ( ) Thus, (, 4.5] [ 7, 6) Thus, (, 3) ( 5, ) = (, 6). = ( 5, 3).

) ( ) Thus, (, 4.5] [ 7, 6) Thus, (, 3) ( 5, ) = (, 6). = ( 5, 3). 152 Sect 10.1 - Compound Inequalities Concept #1 Union and Intersection To understand the Union and Intersection of two sets, let s begin with an example. Let A = {1, 2,,, 5} and B = {2,, 6, 8}. Union

More information

Phases of the Moon. Preliminaries:

Phases of the Moon. Preliminaries: Phases of the Moon Sometimes when we look at the Moon in the sky we see a small crescent. At other times it appears as a full circle. Sometimes it appears in the daylight against a bright blue background.

More information

IT S STRING THEORY, BABY! by Herbert M. Midgley 2006 by Herbert Midgley All Rights Reserved

IT S STRING THEORY, BABY! by Herbert M. Midgley 2006 by Herbert Midgley All Rights Reserved IT S STRING THEORY, BABY! TIME: Present by Herbert M. Midgley 2006 by Herbert Midgley All Rights Reserved PLACE: A garden in the South CHARACTERS: A pretty girl in her late 20 s. She was raised in a small

More information

The Seasons on a Planet like Earth

The Seasons on a Planet like Earth The Seasons on a Planet like Earth As the Earth travels around the Sun, it moves in a giant circle 300 million kilometers across. (Well, it is actually a giant ellipse but the shape is so close to that

More information

Top Ten Mistakes in the FCE Writing Paper (And How to Avoid Them) By Neil Harris

Top Ten Mistakes in the FCE Writing Paper (And How to Avoid Them) By Neil Harris Top Ten Mistakes in the FCE Writing Paper (And How to Avoid Them) By Neil Harris Top Ten Mistakes in the FCE Writing Paper (And How to Avoid Them) If you re reading this article, you re probably taking

More information

My Name Is Chris Curry... And I'd Like To Make

My Name Is Chris Curry... And I'd Like To Make My Name Is Chris Curry... And I'd Like To Make A Confession I sold real estate the hard way for way too long. You see, I thought the key to improving my business was working harder. So I worked harder.

More information

MULTIPLICATION AND DIVISION OF REAL NUMBERS In this section we will complete the study of the four basic operations with real numbers.

MULTIPLICATION AND DIVISION OF REAL NUMBERS In this section we will complete the study of the four basic operations with real numbers. 1.4 Multiplication and (1-25) 25 In this section Multiplication of Real Numbers Division by Zero helpful hint The product of two numbers with like signs is positive, but the product of three numbers with

More information

Lesson 26: Reflection & Mirror Diagrams

Lesson 26: Reflection & Mirror Diagrams Lesson 26: Reflection & Mirror Diagrams The Law of Reflection There is nothing really mysterious about reflection, but some people try to make it more difficult than it really is. All EMR will reflect

More information

Chapter 8 Introduction to Hypothesis Testing

Chapter 8 Introduction to Hypothesis Testing Chapter 8 Student Lecture Notes 8-1 Chapter 8 Introduction to Hypothesis Testing Fall 26 Fundamentals of Business Statistics 1 Chapter Goals After completing this chapter, you should be able to: Formulate

More information

I CAN DO IT LYRICS. I put my heart and my mind to it And I can do it.

I CAN DO IT LYRICS. I put my heart and my mind to it And I can do it. I CAN DO IT LYRICS 1)ICAN DO IT Hello boys and girls, it s so good to see your face I love to come to this happy place Where we sing and laugh and learn and play Let s put one thumb up, two thumbs up Point

More information

1974 Rubik. Rubik and Rubik's are trademarks of Seven Towns ltd., used under license. All rights reserved. Solution Hints booklet

1974 Rubik. Rubik and Rubik's are trademarks of Seven Towns ltd., used under license. All rights reserved. Solution Hints booklet # # R 1974 Rubik. Rubik and Rubik's are trademarks of Seven Towns ltd., used under license. All rights reserved. Solution Hints booklet The Professor s Cube Solution Hints Booklet The Greatest Challenge

More information

Point to the completed Venn diagram from the Comprehension Instructional Routine: Compare and Contrast Characters as you discuss it.

Point to the completed Venn diagram from the Comprehension Instructional Routine: Compare and Contrast Characters as you discuss it. Comprehension Instructional Routine: Compare and Contrast Two Settings in One Text Preparation/Materials: chart with signal words, one large text of The Cousins for the teacher, student copies of The Cousins,

More information

Protect Your Business

Protect Your Business www.smallbusinessmarketingaustralia.com Bronwyn@smallbusinessmarketingaustralia.com www.smallbusinessmarketingaustralia.com Page 1 What is Your Online Reputation? Your online image is NOT just your business

More information

Order of Operations More Essential Practice

Order of Operations More Essential Practice Order of Operations More Essential Practice We will be simplifying expressions using the order of operations in this section. Automatic Skill: Order of operations needs to become an automatic skill. Failure

More information

Grade 4 Mathematics Number and Number Relations : Lesson 9

Grade 4 Mathematics Number and Number Relations : Lesson 9 Grade 4 Mathematics Number and Number Relations : Lesson 9 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all

More information

Worksheet Motion of the Sun and Moon

Worksheet Motion of the Sun and Moon Worksheet Motion of the Sun and Moon Apparent Motion of the Sun 1. The Earth makes one complete orbit around the Sun in one year. From the point of view of someone on the Earth this makes the Sun appear

More information

Communication skills at work an introduction

Communication skills at work an introduction 1 Communication skills at work an introduction this chapter covers... This chapter is an introduction to the Applied business communications and personal skills Unit it explains how all the parts of the

More information

THE LANGUAGE OF SETS AND SET NOTATION

THE LANGUAGE OF SETS AND SET NOTATION THE LNGGE OF SETS ND SET NOTTION Mathematics is often referred to as a language with its own vocabulary and rules of grammar; one of the basic building blocks of the language of mathematics is the language

More information

May 25th, 2016--"Car Buying: How to Avoid the Extra Stress"--Mary Dittfurth

May 25th, 2016--Car Buying: How to Avoid the Extra Stress--Mary Dittfurth May 25th, 2016--"Car Buying: How to Avoid the Extra Stress"--Mary Dittfurth The car-buying process can get pretty stressful, especially if you re not prepared for it. Car buying is supposed to be exciting,

More information

Lottery Looper. User Manual

Lottery Looper. User Manual Lottery Looper User Manual Lottery Looper 1.7 copyright Timersoft. All rights reserved. http://www.timersoft.com The information contained in this document is subject to change without notice. This document

More information

Lesson 2: How to Give Compliments to Tutees

Lesson 2: How to Give Compliments to Tutees Kids As Reading Helpers: A Peer Tutor Training Manual Copyright 2002 by Jim Wright www.interventioncentral.org L2-1 Lesson 2: How to Give Compliments to Tutees Introduction When correctly used, compliments

More information

Announcements. CompSci 230 Discrete Math for Computer Science Sets. Introduction to Sets. Sets

Announcements. CompSci 230 Discrete Math for Computer Science Sets. Introduction to Sets. Sets CompSci 230 Discrete Math for Computer Science Sets September 12, 2013 Prof. Rodger Slides modified from Rosen 1 nnouncements Read for next time Chap. 2.3-2.6 Homework 2 due Tuesday Recitation 3 on Friday

More information

NS6-50 Dividing Whole Numbers by Unit Fractions Pages 16 17

NS6-50 Dividing Whole Numbers by Unit Fractions Pages 16 17 NS6-0 Dividing Whole Numbers by Unit Fractions Pages 6 STANDARDS 6.NS.A. Goals Students will divide whole numbers by unit fractions. Vocabulary division fraction unit fraction whole number PRIOR KNOWLEDGE

More information

How to Study Mathematics Written by Paul Dawkins

How to Study Mathematics Written by Paul Dawkins How to Study Mathematics Written by Paul Dawkins Before I get into the tips for how to study math let me first say that everyone studies differently and there is no one right way to study for a math class.

More information

Lecture 16 : Relations and Functions DRAFT

Lecture 16 : Relations and Functions DRAFT CS/Math 240: Introduction to Discrete Mathematics 3/29/2011 Lecture 16 : Relations and Functions Instructor: Dieter van Melkebeek Scribe: Dalibor Zelený DRAFT In Lecture 3, we described a correspondence

More information

The Design Process Of Creating A $40,000 Creative Newspaper Advertisement

The Design Process Of Creating A $40,000 Creative Newspaper Advertisement The Design Process Of Creating A $40,000 Creative Newspaper Advertisement Posted on August 13, 2008 Archived under University along with 73 JUST Creative Comments This semester at University I am studying

More information

01 - The minister is dead. The minister is dead Did you see it on the TV Did you hear it on the radio And do you care what so ever

01 - The minister is dead. The minister is dead Did you see it on the TV Did you hear it on the radio And do you care what so ever 01 - The minister is dead The minister is dead Did you see it on the TV Did you hear it on the radio And do you care what so ever Did he attack our society Or did he just kill one person Did he just raise

More information

Vieta s Formulas and the Identity Theorem

Vieta 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 information

Crossing the Red Sea

Crossing the Red Sea Unit 4: Lesson 3 Please note that these files are subject to copyright, and each Sunday School must own a copy of the Teaching Little Ones: Introducing the Bible CD-ROM in order to use these files. Please

More information

Chorus (x2) Chorus (x2)

Chorus (x2) Chorus (x2) Inequalities Algebra 5.0 Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step. Mr. Queen,

More information

Formal Languages and Automata Theory - Regular Expressions and Finite Automata -

Formal Languages and Automata Theory - Regular Expressions and Finite Automata - Formal Languages and Automata Theory - Regular Expressions and Finite Automata - Samarjit Chakraborty Computer Engineering and Networks Laboratory Swiss Federal Institute of Technology (ETH) Zürich March

More information

Fractions Packet. Contents

Fractions Packet. Contents Fractions Packet Contents Intro to Fractions.. page Reducing Fractions.. page Ordering Fractions page Multiplication and Division of Fractions page Addition and Subtraction of Fractions.. page Answer Keys..

More information

Light of the World: Salt of the Earth

Light of the World: Salt of the Earth Light of the World: Salt of the Earth Teacher Pep Talk: Jesus said You are the light of the world. That seems to be an exciting reality and a daunting challenge, all at the same time. It also raises several

More information

7. 080207a, P.I. A.A.17

7. 080207a, P.I. A.A.17 Math A Regents Exam 080 Page 1 1. 08001a, P.I. A.A.6 On a map, 1 centimeter represents 40 kilometers. How many kilometers are represented by 8 centimeters? [A] 48 [B] 30 [C] 5 [D] 80. 0800a, P.I. G.G.38

More information

Pigeonhole Principle Solutions

Pigeonhole Principle Solutions Pigeonhole Principle Solutions 1. Show that if we take n + 1 numbers from the set {1, 2,..., 2n}, then some pair of numbers will have no factors in common. Solution: Note that consecutive numbers (such

More information

Angela the cat Copyright by AmigurumiBB Vanja Grundmann

Angela the cat Copyright by AmigurumiBB Vanja Grundmann Angela the cat 1 Abbreviations: Ch:Chain St:Stitch Sc:Single crochet Inv.dec.:Invisible decrease Hdc:Half double crochet stitch Sl.st.:Sip stitch Doll is made in spiral. No chain or slip stitch connections

More information

Graduate Management Admission Test (GMAT) Quantitative Section

Graduate Management Admission Test (GMAT) Quantitative Section Graduate Management Admission Test (GMAT) Quantitative Section In the math section, you will have 75 minutes to answer 37 questions: A of these question are experimental and would not be counted toward

More information

Science and Religion

Science and Religion 1 Science and Religion Scripture: Colossians 1:15-20 By Pastor John H. Noordhof Williamsburg Christian Reformed Church October 21, 2012 Morning Service People of God: Today we will deal with the troubling

More information

Lesson 4. Factors and Multiples. Objectives

Lesson 4. Factors and Multiples. Objectives Student Name: Date: Contact Person Name: Phone Number: Lesson 4 Factors and Multiples Objectives Understand what factors and multiples are Write a number as a product of its prime factors Find the greatest

More information

Common Emailing Phrases

Common Emailing Phrases Common Emailing Phrases Pick phrases from below and try to imagine an email to someone in your context using that phrase or those phrases, using your own ideas where there is. Use several phrases in the

More information

3PK. September 5-6, 2015. Samuel. God talks to us. 1 Samuel 3

3PK. September 5-6, 2015. Samuel. God talks to us. 1 Samuel 3 3PK September 5-6, 2015 1 Samuel 3 First 10 minutes of the service hour: Engage kids in cooperative play activities to help them connect to other kids Next 5 minutes: Connect Time Samuel God talks to us.

More information

Lecture 1. Basic Concepts of Set Theory, Functions and Relations

Lecture 1. Basic Concepts of Set Theory, Functions and Relations September 7, 2005 p. 1 Lecture 1. Basic Concepts of Set Theory, Functions and Relations 0. Preliminaries...1 1. Basic Concepts of Set Theory...1 1.1. Sets and elements...1 1.2. Specification of sets...2

More information

Chunking? Sounds like psychobabble!

Chunking? Sounds like psychobabble! Chunking? Sounds like psychobabble! By Sarah Frossell Published in Rapport Magazine Winter 1998 So much of the business world depends on the fast, free flow of information but does the unit size the information

More information

Getting Started with WebSite Tonight

Getting Started with WebSite Tonight Getting Started with WebSite Tonight WebSite Tonight Getting Started Guide Version 3.0 (12.2010) Copyright 2010. All rights reserved. Distribution of this work or derivative of this work is prohibited

More information

Using sentence fragments

Using sentence fragments Lesson 8 Descriptive Essays Description is not a distinct mode of writing, like expository, narrative, and persuasive, but the ability to write descriptively is essential to a host of writing genres. Many

More information

Singing and Motions. one year old

Singing and Motions. one year old Singing and Motions inging simple songs to and with your child can help her learn and remember words. Pick a simple child s song and sing it to your child throughout the day and week. Sing it slowly and

More information

Need to Grow Your Business Fast? Steal These 3 Proven Email Marketing Templates to Double Your Sales on Autopilot (No matter what you re selling)

Need to Grow Your Business Fast? Steal These 3 Proven Email Marketing Templates to Double Your Sales on Autopilot (No matter what you re selling) Need to Grow Your Business Fast? Steal These 3 Proven Email Marketing Templates to Double Your Sales on Autopilot (No matter what you re selling) It s no secret Every new entrepreneur and business owner

More information

Finding the last cell in an Excel range Using built in Excel functions to locate the last cell containing data in a range of cells.

Finding the last cell in an Excel range Using built in Excel functions to locate the last cell containing data in a range of cells. Finding the last cell in an Excel range Using built in Excel functions to locate the last cell containing data in a range of cells. There are all sorts of times in Excel when you will need to find the

More information

Ohio s Assessment System

Ohio s Assessment System hio Department of Education Student Name: Ohio s Assessment System Grade 2 Reading Student Booklet Form A Diagnostic Measure 3rd Edition Office of Curriculum and Assessment Copyright 2012 by the Ohio Department

More information

Equations, Lenses and Fractions

Equations, Lenses and Fractions 46 Equations, Lenses and Fractions The study of lenses offers a good real world example of a relation with fractions we just can t avoid! Different uses of a simple lens that you may be familiar with are

More information

1 2-3 Trees: The Basics

1 2-3 Trees: The Basics CS10: Data Structures and Object-Oriented Design (Fall 2013) November 1, 2013: 2-3 Trees: Inserting and Deleting Scribes: CS 10 Teaching Team Lecture Summary In this class, we investigated 2-3 Trees in

More information

STOP for science. Light is a wave. Like waves in water, it can be characterized by a wavelength.

STOP for science. Light is a wave. Like waves in water, it can be characterized by a wavelength. INTRODUCTION Most students have encountered rainbows, either spotting them directly on those special days when the raindrops fall while the Sun still finds cloudless regions to peek through, or at least

More information

Fulbrook Middle School 8 th Year Assignment Homework. Is Pluto a Planet?

Fulbrook Middle School 8 th Year Assignment Homework. Is Pluto a Planet? Fulbrook Middle School 8 th Year Assignment Homework Is Pluto a Planet? Is Pluto a Planet? In 2005 a new object was discovered in the Solar system, this was named Eris. Scientists were wondering if they

More information

$25,000 CHILDREN'S LIFE INSURANCE

$25,000 CHILDREN'S LIFE INSURANCE PMS 294 BLUE & PMS158 ORANGE ON WHITE PAPER E-2454 Globe Life And Accident Insurance Company Globe Life Center Oklahoma City, OK 73184 PRSRT STD U.S. POSTAGE PAID GMS $25,000 CHILDREN'S LIFE INSURANCE

More information

Pool Border Task. The Mathematics of the Task

Pool Border Task. The Mathematics of the Task Pool Border Task How many unit square tiles does it take to build a border around a square pool? The length of the sides of the pool is a natural number of units (1, 2, 3,...) and the border is just one

More information

Jamberry Nails Home Party Script

Jamberry Nails Home Party Script Jamberry Nails Home Party Script There are 7 Key Elements for each Jamberry Nails home party: 1. Meet & Greet 2. The Opening Talk 3. Sharing the Products (The Presentation personal demo) 4. Booking Talk

More information

Ethical Decision-Making Model

Ethical Decision-Making Model t General Dynamics, we face business ethics decisions almost every day. Many are straightforward and require little conscious thought to resolve: doing the right thing just comes naturally. ome, however,

More information