Set operations and Venn Diagrams. COPYRIGHT 2006 by LAVON B. PAGE


 Annabelle Atkinson
 1 years ago
 Views:
Transcription
1 Set operations and Venn Diagrams
2 Set operations and Venn diagrams! = { x x " and x " } This is the intersection of and. # = { x x " or x " } This is the union of and. n element of! belongs to both and, an element of # is required to belong to at least one of the sets.
3 ! = { x x " and x " }
4 # = { x x " or x " }
5 Sets and the Universal Set = {1,2,3,4}, = {1,3,5,7}, and C = {7,9,3}, and the universal set U = {1,2,3,4,5,6,7,8,9}. Locate all this information appropriately in a Venn diagram.
6 Sets and the Universal Set = {1,2,3,4}, = {1,3,5,7}, and C = {7,9,3}, and the universal set U = {1,2,3,4,5,6,7,8,9}. Locate all this information appropriately in a Venn diagram. With each number, place it in the appropriate region. C
7 Sets and the Universal Set = {1,2,3,4}, = {1,3,5,7}, and C = {7,9,3}, and the universal set U = {1,2,3,4,5,6,7,8,9}. Locate all this information appropriately in a Venn diagram. With each number, place it in the appropriate region. 1 C
8 Sets and the Universal Set = {1,2,3,4}, = {1,3,5,7}, and C = {7,9,3}, and the universal set U = {1,2,3,4,5,6,7,8,9}. Locate all this information appropriately in a Venn diagram. With each number, place it in the appropriate region. 2 1 C
9 Sets and the Universal Set = {1,2,3,4}, = {1,3,5,7}, and C = {7,9,3}, and the universal set U = {1,2,3,4,5,6,7,8,9}. Locate all this information appropriately in a Venn diagram. With each number, place it in the appropriate region C
10 Sets and the Universal Set = {1,2,3,4}, = {1,3,5,7}, and C = {7,9,3}, and the universal set U = {1,2,3,4,5,6,7,8,9}. Locate all this information appropriately in a Venn diagram. With each number, place it in the appropriate region. Check out the Venn diagram and make sure you agree with where all the elements have been placed C
11 Distributive Law for Unions # (! C) = ( # )! ( # C)
12 Distributive Law for Unions # (! C) = ( # )! ( # C) C
13 Distributive Law for Unions # (! C) = ( # )! ( # C) C ( # )! ( # C)
14 Distributive Law for Unions # (! C) = ( # )! ( # C) C # (! C) C ( # )! ( # C)
15 Distributive Law for Unions # (! C) = ( # )! ( # C) C # (! C) C ( # )! ( # C)
16 DeMorgan s Law ( # ) c = c! c
17 DeMorgan s Law ( # ) c = c! c ( # ) c is the gray region in this picture
18 DeMorgan s Law ( # ) c = c! c ( # ) c is the gray region in this picture t this stage is painted green.
19 DeMorgan s Law ( # ) c = c! c ( # ) c is the gray region in this picture Now is painted red, so what s outside of and outside of hasn t been painted.
20 DeMorgan s Law ( # ) c = c! c ( # ) c is the gray region in this picture What hasn t been painted is c! c
21 DeMorgan s Other Law (! ) c = c # c
22 DeMorgan s Other Law (! ) c = c # c
23 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (a) students studying math but not business
24 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (a) students studying math but not business M! c
25 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (b) students studying both math and business
26 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (b) students studying both math and business M!
27 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (c) students studying either math or business
28 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (c) students studying either math or business M #
29 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (d) students who study neither math nor business
30 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (d) students who study neither math nor business (M # ) c or M c! c
31 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (e) students who don t study math and who don t study business
32 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (e) students who don t study math and who don t study business (M # ) c or M c! c
33 Sketching regions representing sets: Sketch the region corresponding to the set ( # c )! C C
34 Sketching regions representing sets: Sketch the region corresponding to the set ( # c )! C C
35 Sketching regions representing sets: Sketch the region corresponding to the set ( # c )! C C
36 Sketching regions representing sets: Sketch the region corresponding to the set ( # c )! C C
Section 1.5: Venn Diagrams  Shading
Section 1.5: Venn Diagrams  Shading A Venn diagram is a way to graphically represent sets and set operations. Each Venn diagram begins with a rectangle representing the universal set. Then each set is
More informationA Set A set is a collection of objects. The objects are called members or elements. The elements may have something in common or may be unrelated.
A Set A set is a collection of objects. The objects are called members or elements. The elements may have something in common or may be unrelated. A = {5, 10, 15, 20, 25} B = {prime numbers less than 20}
More information1.1 Introduction to Sets
1.1 Introduction to Sets A set is a collection of items. These items are referred to as the elements or members of the set. We usually use uppercase letters, such as A and B, to denote sets. We can write
More informationMATH0201 BASIC CALCULUS
MATH0201 BASIC CALCULUS Set Dr. WONG Chi Wing Department of Mathematics, HKU Definition 1 A set is a well defined collection of objects, i.e., we can determine whether a given object belongs to that set
More informationPART 1 MODULE 2 SET OPERATIONS, VENN DIAGRAMS
PART 1 MODULE 2 SET OPERATIONS, VENN DIAGRAMS SET OPERATIONS Let U = {x x is an Englishlanguage film} Set A below contains the five best films according to the American Film Institute. A = {Citizen Kane,
More informationChapter 2 Sets and Counting
Chapter 2 Sets and Counting Sets Learn the following: Definition of a set, subset, element of a set, null set, cardinal number of a set, set notations, operations on sets (union, intersection, difference,
More informationThese are based on 45/50 minute lessons. Lesson No. Suggested Plan References 1. Logic Puzzles 1 Introducing interactive example OS 1.
St These are based on 45/50 minute lessons. 1. Logic Puzzles 1 Introducing interactive example OS 1.1 PB 1.1, Q1 PB 1.1, Q2 and Q4 Discuss solutions to Q2 and Q4 PB 1.1, Q3 and Q6 2. Logic Puzzles 2 Mental
More informationMathematics for Economists (66110) Lecture Notes 1
Mathematics for Economists (66110) Lecture Notes 1 Sets Definition: set is a collection of distinct items The items in a set are called elements of the set Examples: 1) The set of integers greater than
More informationM2L3. Axioms of Probability
M2L3 Axioms of Probability 1. Introduction This lecture is a continuation of discussion on random events that started with definition of various terms related to Set Theory and event operations in previous
More informationClicker Question. Theorems/Proofs and Computational Problems/Algorithms MC215: MATHEMATICAL REASONING AND DISCRETE STRUCTURES
MC215: MATHEMATICAL REASONING AND DISCRETE STRUCTURES Tuesday, 1/21/14 General course Information Sets Reading: [J] 1.1 Optional: [H] 1.11.7 Exercises: Do before next class; not to hand in [J] pp. 1214:
More informationLecture 2. Text: A Course in Probability by Weiss 2.4. STAT 225 Introduction to Probability Models January 15, Whitney Huang Purdue University
Lecture 2 s; Text: A Course in Probability by Weiss 2.4 STAT 225 Introduction to Probability Models January 15, 2014 s; Whitney Huang Purdue University 2.1 Agenda s; 1 2 2.2 Set Operations s; Intersection:
More informationMath 117 Chapter 7 Sets and Probability
Math 117 Chapter 7 and Probability Flathead Valley Community College Page 1 of 15 1. A set is a welldefined collection of specific objects. Each item in the set is called an element or a member. Curly
More information2. The plane, sets, and more notation
Maths for Economics 2. The plane, sets, and more notation Vera L. te Velde 25. August 2015 1 The Cartesian plane Often times we want to talk about pairs of numbers. We can visualize those by combining
More informationMATH 105: Finite Mathematics 62: The Number of Elements in a Set
MATH 105: Finite Mathematics 62: The Number of Elements in a Set Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006 Outline 1 Counting with Venn Diagrams 2 Story Problems 3 Conclusion Outline
More informationL01  Set Theory. CSci/Math May 2015
L01  Set Theory CSci/Math 2112 06 May 2015 1 / 10 Elements and Subsets of a Set a A means a is an element of the set A a / A means a is not an element of the set A A B means A is a subset of B (all elements
More informationLESSON SUMMARY. Set Operations and Venn Diagrams
LESSON SUMMARY CXC CSEC MATHEMATICS UNIT Three: Set Theory Lesson 4 Set Operations and Venn Diagrams Textbook: Mathematics, A Complete Course by Raymond Toolsie, Volumes 1 and 2. (Some helpful exercises
More informationChapter Sets. Section 2 Sets. Set Properties and Set Notation (continued) Set Properties and Set Notation
Chapter 7 Logic, Sets, and Counting 7.2 Sets This section will discuss the symbolism and concepts of set theory. Section 2 Sets 2 Set Properties and Set Notation Set Properties and Set Notation Definition:
More informationName Date. Goal: Understand and represent the intersection and union of two sets.
F Math 12 3.3 Intersection and Union of Two Sets p. 162 Name Date Goal: Understand and represent the intersection and union of two sets. A. intersection: The set of elements that are common to two or more
More informationหล กการจ าแนกประเภทรายจ ายตามงบประมาณ
กร ณาด รายละเอ ยด งบบ คลากร ท ม การปร บปร ง ตามหน งส อสาน กงบประมาณ ท นร 0702/ว 45 ลงว นท 25 ม.ค. 2547 เร อง การปร บปร งหล กการจาแนกประเภทรายจ ายตามงบประมาณ ประกอบด วย หล กการจ าแนกประเภทรายจ ายตามงบประมาณ
More informationTopic 7: Venn Diagrams, Sets, and Set Notation
Topic 7: Venn Diagrams, Sets, and Set Notation for use after What Do You Expect? Investigation 1 set is a collection of objects. These objects might be physical things, like desks in a classroom, or ideas,
More informationMath 10 Chapter 2 Handout Helene Payne. Name:
Name: Sets set is a welldefined collection of distinct objects. Welldefined means that we can determine whether an object is an element of a set or not. Distinct means that we can tell the objects apart.
More informationSet Theory: Topics of Study: Set Notation: Roster notation, setbuilder notation, interval Notation. Set Notation: Operations with sets
Set Theory: Topics of Study: Set Notation: Roster notation, setbuilder notation, interval Notation Set Notation: Operations with sets Union, Intersection, and Complement Videos to introduce set theory
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 informationGRADE 7 MATH LEARNING GUIDE
GRDE 7 MTH Lesson 2.1: Union and Intersection of Sets Time: 1.5 hours Prerequisite Concepts: Whole Numbers, definition of sets, Venn diagrams bout the Lesson: fter learning some introductory concepts
More informationHawkes Learning Systems: College Algebra
Hawkes Learning Systems: College Algebra Section 1.2: The Arithmetic of Algebraic Expressions Objectives o Components and terminology of algebraic expressions. o The field properties and their use in algebra.
More informationIB Math Studies Topic 3 Day 1 Introduction to Sets. Sets are denoted with a capital letter. The items, names, objects or numbers are enclosed by { }.
I Math Studies Topic 3 Day 1 Introduction to Sets Name Date lock set is. SET NOTTION Sets are denoted with a capital letter. The items, names, objects or numbers are enclosed by { }. is the symbol denoting
More informationSome Definitions about Sets
Some Definitions about Sets Definition: Two sets are equal if they contain the same elements. I.e., sets A and B are equal if x[x A x B]. Notation: A = B. Recall: Sets are unordered and we do not distinguish
More informationVenn Diagrams and Set Operations
Survey of Math  MT 140 Page: 1 Venn Diagrams and Set Operations 1 Operations on Sets 1.1 Compliment Compliment of a Set  all the elements in the niverse that are NOT in the given set. Notation 0 in English
More informationCmSc 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 informationMath/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 informationGRADE 7 MATH LEARNING GUIDE
GRADE 7 MATH LESSON 12: SUBSETS OF REAL NUMBERS Time: 1.5 hours Prerequisite Concepts: whole numbers and operations, set of integers, rational numbers, irrational numbers, sets and set operations, Venn
More informationSet Theory: Venn Diagrams for Problem Solving
Set Theory: Venn Diagrams for Problem Solving In addition to just being fun, we can also use Venn diagrams to solve problems. When doing so, the key is to work from the inside out, meaning we start by
More informationEXAM. Exam #3. Math 1430, Spring 2002. April 21, 2001 ANSWERS
EXAM Exam #3 Math 1430, Spring 2002 April 21, 2001 ANSWERS i 60 pts. Problem 1. A city has two newspapers, the Gazette and the Journal. In a survey of 1, 200 residents, 500 read the Journal, 700 read the
More informationThe Language of Mathematics
CHPTER 2 The Language of Mathematics 2.1. Set Theory 2.1.1. Sets. set is a collection of objects, called elements of the set. set can be represented by listing its elements between braces: = {1, 2, 3,
More informationI. Mathematical Statements and Proofs
These are supplementary notes for Week 1 s lectures. It does not cover all of the material discussed in lectures, but rather is intended to provided extra explanations of material related to the lectures.
More informationTest 1 Math 221: Basic Concepts of Elementary Mathematics I
Test 1 Math 221: Basic Concepts of Elementary Mathematics I Name Instructions: Check that your test consists of 25 problems. Put your name in the space provided above. Answer each multiple choice question
More informationSets 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 informationBasics of Set Theory and Logic. Set Theory
Basics of Set Theory Logic S. F. Ellermeyer August 18, 2000 Membership Set Theory A set is a welldefined collection of objects. Any object which is in a set is called a member of the set. If the object
More informationThe Mathematics Driving License for Computer Science CS10410
The Mathematics Driving License for Computer Science CS10410 Venn Diagram, Union, Intersection, Difference, Complement, Disjoint, Subset and Power Set Nitin Naik Department of Computer Science VennEuler
More informationLecture 1. Basic Concepts of Set Theory.
V. Borschev and B. Partee, September 6, 2001 p. 1 Lecture 1. Basic Concepts of Set Theory. 0. Goals... 1 1. Basic Concepts of Set Theory.... 1 1.1. Sets and elements... 1 1.2. Specification of sets...
More informationWhat is probability? Sample space and events. Some set theory. Math 324 Lecture 5 Dr Bolstad
Math 324 Lecture 5 Dr Bolstad http://math324sfsu.bmbolstad.com What is probabilit? Probabilit is the stud of randomness and uncertainit. Probabilit allows us to quantif the chance that a certain event
More informationLesson Problem Solving Classify Plane Shapes Essential Question How can you use the strategy draw a diagram to classify plane shapes?
Name Problem Solving Classify Plane Shapes Essential Question How can you use the strategy draw a diagram to classify plane shapes? Unlock the Problem PROBLEM SOLVING Lesson 12.8 Geometry 3.G.A.1 MATHEMATICAL
More informationSets. Another example of a set is the set of all positive whole numbers between (and including) 1 and 10. Let this set be defined as follows. .
Sets A set is simply a collection of objects. For example the set of the primary colours of light include red, green and blue. In set notation, a set is often denoted by a letter and the members or elements
More informationA Little Set Theory (Never Hurt Anybody)
A Little Set Theory (Never Hurt Anybody) Matthew Saltzman Department of Mathematical Sciences Clemson University Draft: August 21, 2013 1 Introduction The fundamental ideas of set theory and the algebra
More informationCompound Inequalities. Section 36
Compound Inequalities Section 36 Goals Goal To solve and graph inequalities containing the word and. To solve and graph inequalities containing the word or. Vocabulary Compound Inequality Interval Notation
More informationIntroduction Russell s Paradox Basic Set Theory Operations on Sets. 6. Sets. Terence Sim
6. Sets Terence Sim 6.1. Introduction A set is a Many that allows itself to be thought of as a One. Georg Cantor Reading Section 6.1 6.3 of Epp. Section 3.1 3.4 of Campbell. Familiar concepts Sets can
More informationGRADE 7 MATH TEACHING GUIDE
GRDE 7 MTH Lesson 2.1: Union and Intersection of Sets Prerequisite Concepts: Whole Numbers, definition of sets, Venn diagrams Objectives: In this lesson, you are expected to: 1. Describe and define a.
More informationProbability  Part I. Definition : A random experiment is an experiment or a process for which the outcome cannot be predicted with certainty.
Probability  Part I Definition : A random experiment is an experiment or a process for which the outcome cannot be predicted with certainty. Definition : The sample space (denoted S) of a random experiment
More informationSections 2.1, 2.2 and 2.4
SETS Sections 2.1, 2.2 and 2.4 Chapter Summary Sets The Language of Sets Set Operations Set Identities Introduction Sets are one of the basic building blocks for the types of objects considered in discrete
More informationMATH 105: Finite Mathematics 72: Properties of Probability
MATH 105: Finite Mathematics 72: Properties of Probability Prof. Jonathan Duncan Walla Walla College Winter Quarter, 2006 Outline 1 Probability of Combined Events 2 Probability and Venn Diagrams 3 Odds
More informationNotations:, {...} a S means that a is an element of S. a S means that a is not an element of S
Set Theory 1 Notations:, {....} Let S be a set (a collection of elements, with no duplicates) a S means that a is an element of S Example: 1 {1,2,3}, 3 {1,2,3} a S means that a is not an element of S Example:
More informationPROBABILITY INTERMEDIATE GROUP OCTOBER 23, 2016
PROBABILITY INTERMEDIATE GROUP OCTOBER 23, 2016 What is probability? Probability measures the likelihood of different possible outcomes by assigning each outcome a number between 0 and 1. The higher the
More information4 Sets and Operations on Sets
4 Sets and Operations on Sets The languages of set theory and basic set operations clarify and unify many mathematical concepts and are useful for teachers in understanding the mathematics covered in elementary
More informationContents REASONING AND PROOF INEQUALITIES AND LINEAR PROGRAMMING
Contents UNIT 1 REASONING AND PROOF Lesson 1 Reasoning Strategies...................... 2 1 Reasoned Arguments............................. 3 2 Reasoning with IfThen Statements...................... 10
More informationThe Joy of Sets. Joshua Knowles. Introduction to Maths for Computer Science, School of Computer Science University of Birmingham
School of Computer Science University of Birmingham Introduction to Maths for Computer Science, 2015 Definition of a Set A set is a collection of distinct things. We generally use upper case letters to
More informationChapter 1. Open Sets, Closed Sets, and Borel Sets
1.4. Borel Sets 1 Chapter 1. Open Sets, Closed Sets, and Borel Sets Section 1.4. Borel Sets Note. Recall that a set of real numbers is open if and only if it is a countable disjoint union of open intervals.
More informationEvents, Sample Space, Probability, and their Properties
3.1 3.4 Events, Sample Space, Probability, and their Properties Key concepts: events, sample space, probability Probability is a branch of mathematics that deals with modeling of random phenomena or experiments,
More informationProbability. Mathematics Help Sheet. The University of Sydney Business School
Probability Mathematics Help Sheet The University of Sydney Business School Introduction What is probability? Probability is the expression of knowledge or belief about the chance of something occurring.
More informationSection 2.3: Rational Functions
CHAPTER Polynomial and Rational Functions Section.3: Rational Functions Asymptotes and Holes Graphing Rational Functions Asymptotes and Holes Definition of a Rational Function: Definition of a Vertical
More informationMath 166  Week in Review #4. A proposition, or statement, is a declarative sentence that can be classified as either true or false, but not both.
Math 166 Spring 2007 c Heather Ramsey Page 1 Math 166  Week in Review #4 Sections A.1 and A.2  Propositions, Connectives, and Truth Tables A proposition, or statement, is a declarative sentence that
More informationFirst Problem Assignment
First Problem ssignment EES 401 PROLEM 1 (15 points) Fully explain your answers to the following questions. Due on January 12, 2007 (a) If events and are mutually exclusive and collectively exhaustive,
More informationSETS. Chapter Overview
Chapter 1 SETS 1.1 Overview This chapter deals with the concept of a set, operations on sets.concept of sets will be useful in studying the relations and functions. 1.1.1 Set and their representations
More informationAn inequality is a mathematical statement containing one of the symbols <, >, or.
Further Concepts for Advanced Mathematics  FP1 Unit 3 Graphs & Inequalities Section3c Inequalities Types of Inequality An inequality is a mathematical statement containing one of the symbols , or.
More information+ Section 6.0 and 6.1
+ Section 6.0 and 6.1 Introduction to Randomness, Probability, and Simulation Learning Objectives After this section, you should be able to DESCRIBE the idea of probability DESCRIBE myths about randomness
More information7.2 Applications of Venn Diagrams
7.2 Applications of Venn Diagrams In this section, we will see how we can use Venn diagrams to understand or interpret data that may be obtained from real life situations. As in the previous section, we
More informationSection 1.4: Operations on Functions
SECTION 14 Operations on Functions Section 14: Operations on Functions Combining Functions by Addition, Subtraction, Multiplication, Division, and Composition Combining Functions by Addition, Subtraction,
More informationThe Basic Notions of Sets and Functions
The Basic Notions of Sets and Functions Notes for Math 261 Steve Bleiler and Bin Jiang Department of Mathematics and Statistics Portland State University c September 2008 0 Introduction Over the last few
More informationSection 8.0 (Preliminary) Sets, Set Operations & Cardinality
Section 8.0 (Preliminary) Sets, Set Operations & Cardinality A set is simply the grouping together of objects. For example, we count using the set of whole numbers 1, 2, 3, 4, and so forth. We spell words
More information19 Boolean and Set. Algebra. There is a more comprehensive treatment of Boolean Algebra near the top of cargalmathbooks.com
19 Boolean and Set There is a more comprehensive treatment of Boolean Algebra near the top of cargalmathbooks.com Algebra It has been known for sometime in mathematics that set algebras and Boolean 1 algebras
More informationFlorida Department of Education/Office of Assessment January 2012. Algebra 1 EndofCourse Assessment Achievement Level Descriptions
Florida Department of Education/Office of Assessment January 2012 Algebra 1 EndofCourse Assessment Achievement Level Descriptions Algebra 1 EOC Assessment Reporting Category Functions, Linear Equations,
More informationTable of Contents. Sets
Table of Contents SETS... 2 Problem 1: Create Venn Diagram  Coffee or Juice (Easy)... 3 Problem 2: Create Venn Diagram  NCIS or Good Wife (Easy)... 4 Problem 3: Create Venn Diagram  School Survey (Medium)...
More informationKOVÁCS BÉLA, MATHEmATICS I.
KOVÁCS BÉLA, MATHEmATICS I. 1 I. SETS 1. NOTATIOnS The concept and properties of the set are often used in mathematics. We do not define set, as it is an intuitive concept. This is not unusual. You may
More informationSets. A set is a collection of (mathematical) objects, with the collection treated as a single mathematical object.
Sets 1 Sets Informally: A set is a collection of (mathematical) objects, with the collection treated as a single mathematical object. Examples: real numbers, complex numbers, C integers, All students in
More informationCHAPTER 5: PROBABILITY key
Key Vocabulary: trial random probability independence random phenomenon sample space S = {H, T} tree diagram replacement event P(A) Complement A C disjoint Venn Diagram union (or) intersection (and) trial
More informationMath 3000 Running Glossary
Math 3000 Running Glossary Last Updated on: July 15, 2014 The definition of items marked with a must be known precisely. Chapter 1: 1. A set: A collection of objects called elements. 2. The empty set (
More informationTHE 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 informationA set is a Many that allows itself to be thought of as a One. (Georg Cantor)
Chapter 4 Set Theory A set is a Many that allows itself to be thought of as a One. (Georg Cantor) In the previous chapters, we have often encountered sets, for example, prime numbers form a set, domains
More informationSection Sets and Set Operations
Section 6.1  Sets and Set Operations Definition: A set is a welldefined collection of objects usually denoted by uppercase letters. Definition: The elements, or members, of a set are denoted by lowercase
More information4.1. Sets. Introduction. Prerequisites. Learning Outcomes. Learning Style
ets 4.1 Introduction If we can identify a property which is common to several objects, it is often useful to group them together. uch a grouping is called a set. Engineers for example, may wish to study
More informationHOME LEARNING TIMETABLE Year 7 Tutor Groups. HOME LEARNING TIMETABLE Year 7 Tutor Groups
7P English Maths English Maths (Maths) 7R English Maths (Maths) English Maths 7E English Maths (Maths) English Maths 7S English Maths (Maths) English Maths 7T English Maths (Maths) English Maths 201011
More informationMotivation and Applications: Why Should I Study Probability?
Motivation and Applications: Why Should I Study Probability? As stated by Laplace, Probability is common sense reduced to calculation. You need to first learn the theory required to correctly do these
More informationBasic 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 informationLecture 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 informationSets. Chapter 2. A = {1, 0}. The order of elements is irrelevant in a set, so we could write A in an equivalent form as
Chapter 2 Sets Before embarking upon a detailed discussion of statistics, it is useful to introduce some notation to help in describing data. This section introduces elementary set theory notation and
More informationSurvey of Math Mastery Math. Unit 6: Sets
Survey of Math Mastery Math Unit 6: Sets Sets Part 1 Set a well defined collection of objects; The set of all grades you can earn in this class The set of tools in a tool box The set of holiday dishes
More informationSets, Relations and Functions
Sets, Relations and Functions Eric Pacuit Department of Philosophy University of Maryland, College Park pacuit.org epacuit@umd.edu ugust 26, 2014 These notes provide a very brief background in discrete
More informationSet Operations. Set Union. Set Intersection. Set Complement by AH. Esfahanian. All Rights Reserved. 1
Set nion Set Operations Section 2.2 Definition: Let A and B be sets. The union of A and B, denoted A B, is the set containing those elements that are either in A or in B, or in both. Formally, A B = {x
More informationMATH 105: Contemporary Math. Set Theory: Subsets, Venn Diagrams & Set Operations
MATH 105: Contemporary Math Set Theory: Subsets, Venn Diagrams & Set Operations Subsets Set A is a subset of another set B if every element of A is also an element of B. We write: A B (... the symbol 'opens'
More informationFundamentals Part 1 of Hammack
Fundamentals Part 1 of Hammack Dr. Doreen De Leon Math 111, Fall 2014 1 Sets 1.1 Introduction to Sets A set is a collection of things called elements. Sets are sometimes represented by a commaseparated
More informationChapter 4 Introduction to Probability. Learning objectives
Chapter 4 Introduction to Probability Slide 1 Learning objectives 1. Introduction to probability 1.1. Understand experiments, outcomes, sample space. 1.2. How to assign probabilities to outcomes 1.3. Understand
More information1 x if x < 0. 5 x if x > 2. g(2 + ɛ) = 5 (2 + ɛ) = 3 ɛ
Math 4853 Homework Problem Answers 1 Assignment Problem 1.1. Let f(x) : R R be the piecewise linear function defined by: 1 x if x < 0 f(x) = 1 if 0 x 2 5 x if x > 2 (a) Sketch the graph of y = f(x). (b)
More informationVENN DIAGRAMS. Condition #1 Condition #2 A B C. Answer: B and C have reflection symmetry. C and D have at least one pair of parallel sides.
VENN DIAGRAMS VENN DIAGRAMS AND CLASSIFICATIONS A Venn diagram is a tool used to classify objects. It is usually composed of two or more circles that represent different conditions. An item is placed or
More informationPROBABILITY  RULES & DEFINITIONS
ROBABILITY  RULES & DEFINITIONS robability Rules & Definitions In the study of sets, new sets are derived from given sets using the operations of intersection, union, and complementation The same is done
More informationBasics of Probability
Basics of Probability August 27 and September 1, 2009 1 Introduction A phenomena is called random if the exact outcome is uncertain. The mathematical study of randomness is called the theory of probability.
More informationNoteTaking Guides. How to use these documents for success
1 NoteTaking Guides How to use these documents for success Print all the pages for the module. Open the first lesson on the computer. Fill in the guide as you read. Do the practice problems on notebook
More informationLesson 4: The Number System
Lesson 4: The Number System Introduction The next part of your course covers math skills. These lessons have been designed to provide an overview of some basic mathematical concepts. This part of your
More informationLecture 1 (Review of High School Math: Functions and Models) Introduction: Numbers and their properties
Lecture 1 (Review of High School Math: Functions and Models) Introduction: Numbers and their properties Addition: (1) (Associative law) If a, b, and c are any numbers, then ( ) ( ) (2) (Existence of an
More informationGRADE 7 MATH TEACHING GUIDE
GRADE 7 MATH Lesson 12: SUBSETS OF REAL NUMBERS Time: 1.5 hours Prerequisite Concepts: whole numbers and operations, set of integers, rational numbers, irrational numbers, sets and set operations, Venn
More informationPacket: Sets and Venn Diagrams
Packet: Sets and Venn Diagrams Standards covered: *MA.912.D.7.1 Perform set operations such as union and intersection, complement, and cross product. *MA.912.D.7.2 Use Venn diagrams to explore relationships
More informationU Universal set All the elements given in a question Is an element or
Set Theory Set notation Symbol Definition Means U Universal set All the elements given in a question Is an element or Number/object is in the set member of Is not an element of Number/object is not in
More information