Chapter 2 Section 3 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.

Slides:



Advertisements
Similar presentations
Introduction to Set Theory
Advertisements

Slide 2-1 Copyright © 2005 Pearson Education, Inc. SEVENTH EDITION and EXPANDED SEVENTH EDITION.
Chapter 2 The Basic Concepts of Set Theory
Chapter 2 The Basic Concepts of Set Theory
Sets and Venn Diagrams By Amber K. Wozniak.
Survey of Mathematical Ideas Math 100 Chapter 2
2.1 – Symbols and Terminology Definitions: Set: A collection of objects. Elements: The objects that belong to the set. Set Designations (3 types): Word.
Chapter 2 The Basic Concepts of Set Theory © 2008 Pearson Addison-Wesley. All rights reserved.
DP SL Studies Chapter 7 Sets and Venn Diagrams. DP Studies Chapter 7 Homework Section A: 1, 2, 4, 5, 7, 9 Section B: 2, 4 Section C: 1, 2, 4, 5 Section.
MTH 231 Section 2.1 Sets and Operations on Sets. Overview The notion of a set (a collection of objects) is introduced in this chapter as the primary way.
Sets --- A set is a collection of objects. Sets are denoted by A, B, C, … --- The objects in the set are called the elements of the set. The elements are.
Chapter 2 Section 3 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.
Slide Copyright © 2009 Pearson Education, Inc. Welcome to MM150 – Unit 2 Seminar Unit 2 Seminar Instructor: Larry Musolino
Slide Chapter 2 Sets. Slide Set Concepts.
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 2 Set Theory.
Chapter 2 Section 1 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.
Section 2.3B Venn Diagrams and Set Operations
Chapter 2 Section 3 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.
Section 2.2 Subsets and Set Operations Math in Our World.
Unit 2 Sets.
SECTION 2-3 Set Operations and Cartesian Products Slide
Section 2.3 Using Venn Diagrams to Study Set Operations Math in Our World.
Set Operations Chapter 2 Sec 3. Union What does the word mean to you? What does it mean in mathematics?
UNIT VOCABULARY Functions. Closed Form of a Sequence (This is also known as the explicit form of a sequence.) For an arithmetic sequence, use a n = a.
Warning: All the Venn Diagram construction and pictures will be done during class and are not included in this presentation. If you missed class you.
Chapter 2 Section 2 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.
Virtual Field Trip: We’ll visit the Academic Support Center, click “My Studies” on your KU Campus Homepage. The pdf and additional materials about Sets.
Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 2.3 Venn Diagrams and Set Operations.
Section 1.2 – 1.3 Outline Intersection  Disjoint Sets (A  B=  ) AND Union  OR Universe The set of items that are possible for membership Venn Diagrams.
MATH 2311 Section 2.2. Sets and Venn Diagrams A set is a collection of objects. Two sets are equal if they contain the same elements. Set A is a subset.
Sets. The Universal & Complement Sets Let the Universal Set be U U = { 1, 2, 3, 4, 5, 6, 7, 8, 9} and a set A = { 2,3,4,5,6}. Then, the complement.
Chapter 7 Sets and Probability Section 7.1 Sets What is a Set? A set is a well-defined collection of objects in which it is possible to determine whether.
Copyright © 2014, 2010, 2007 Pearson Education, Inc. Section 2.2, Slide 1 Set Theory 2 Using Mathematics to Classify Objects.
Thinking Mathematically Venn Diagrams and Subsets.
Sullivan Algebra and Trigonometry: Section 14.1 Objectives of this Section Find All the Subsets of a Set Find the Intersection and Union of Sets Find the.
Thinking Mathematically Venn Diagrams and Set Operations.
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 2.3, Slide 1 CHAPTER 2 Set Theory.
The Basic Concepts of Set Theory. Chapter 1 Set Operations and Cartesian Products.
Unions and Intersections of Sets Chapter 3 Section 8.
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 2.4, Slide 1 CHAPTER 2 Set Theory.
Union and Intersection of Sets. Definition - intersection The intersection of two sets A and B is the set containing those elements which are and elements.
Venn Diagrams.
Algebra 2 Chapter 12 Venn Diagrams, Permutations, and Combinations Lesson 12.2.
 2012 Pearson Education, Inc. Slide Chapter 2 The Basic Concepts of Set Theory.
The set of whole numbers less than 7 is {1, 2, 3, 4, 5, 6}
CHAPTER 2 Set Theory.
Unions and Intersections of Sets
Venn Diagrams and Set Operation
Venn Diagrams and Subsets
Chapter 2 The Basic Concepts of Set Theory
The Basic Concepts of Set Theory
Section 2.3 Venn Diagrams and Set Operations
Section 2.3B Venn Diagrams and Set Operations
Chapter 2 The Basic Concepts of Set Theory
The Basic Concepts of Set Theory
The Basic Concepts of Set Theory
SEVENTH EDITION and EXPANDED SEVENTH EDITION
CHAPTER 2 Set Theory.
Chapter 2 The Basic Concepts of Set Theory
Chapter Sets &Venn Diagrams.
SETS Sets are denoted by Capital letters Sets use “curly” brackets
2 Chapter Numeration Systems and Sets
Thinking Mathematically
CHAPTER 2 Set Theory.
2.1 – Symbols and Terminology
Thinking Mathematically
VENN DIAGRAMS By Felicia Wright
AND.
CHAPTER 2 Set Theory.
Presentation transcript:

Chapter 2 Section 3 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND

Copyright © 2009 Pearson Education, Inc. Chapter 2 Section 3 - Slide 2 Chapter 2 Sets

Copyright © 2009 Pearson Education, Inc. Chapter 2 Section 3 - Slide 3 WHAT YOU WILL LEARN Methods to indicate sets, equal sets, and equivalent sets Subsets and proper subsets Venn diagrams Set operations such as complement, intersection, union, difference and Cartesian product Equality of sets Application of sets Infinite sets

Copyright © 2009 Pearson Education, Inc. Chapter 2 Section 3 - Slide 4 Section 3 Venn Diagrams and Set Operations

Chapter 2 Section 3 - Slide 5 Copyright © 2009 Pearson Education, Inc. Venn Diagrams A Venn diagram is a technique used for picturing set relationships. A rectangle usually represents the universal set, U.  The items inside the rectangle may be divided into subsets of U and are represented by circles.

Chapter 2 Section 3 - Slide 6 Copyright © 2009 Pearson Education, Inc. Disjoint Sets Two sets which have no elements in common are said to be disjoint. The intersection of disjoint sets is the empty set. Disjoint sets A and B are drawn in this figure. There are no elements in common since there is no overlap- ping area between the two circles.

Chapter 2 Section 3 - Slide 7 Copyright © 2009 Pearson Education, Inc. Overlapping Sets For sets A and B drawn in this figure, notice the overlapping area shared by the two circles. This area represents the elements that are in the intersection of set A and set B.

Chapter 2 Section 3 - Slide 8 Copyright © 2009 Pearson Education, Inc. Complement of a Set The set known as the complement contains all the elements of the universal set which are not listed in the given subset. Symbol: A ´

Chapter 2 Section 3 - Slide 9 Copyright © 2009 Pearson Education, Inc. Intersection The intersection of two given sets contains only those elements common to both of those sets. Symbol:

Chapter 2 Section 3 - Slide 10 Copyright © 2009 Pearson Education, Inc. Union The union of two given sets contains all of the elements for both of those sets. The union “unites”, that is, it brings together everything into one set. Symbol:

Chapter 2 Section 3 - Slide 11 Copyright © 2009 Pearson Education, Inc. Subsets When every element of B is also an element of A. Circle B is completely inside circle A.

Chapter 2 Section 3 - Slide 12 Copyright © 2009 Pearson Education, Inc. Equal Sets When set A is equal to set B, all the elements of A are elements of B, and all the elements of B are elements of A. Both sets are drawn as one circle.

Chapter 2 Section 3 - Slide 13 Copyright © 2009 Pearson Education, Inc. The Meaning of and and or and is generally interpreted to mean intersection A B = { x | x A and x B } or is generally interpreted to mean union A B = { x | x A or x B }

Chapter 2 Section 3 - Slide 14 Copyright © 2009 Pearson Education, Inc. The Relationship Between n(A B), n(A), n(B), n(A B) To find the number of elements in the union of two sets A and B, we add the number of elements in set A and B and then subtract the number of elements common to both sets. n(A B) = n(A) + n(B) – n(A B)

Chapter 2 Section 3 - Slide 15 Copyright © 2009 Pearson Education, Inc. Difference of Two Sets The difference of two sets A and B symbolized by A – B, is the set of elements that belong to set A but not to set B. Region 1 represents the difference of the two sets. BA U IIIIII IV