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.

Slides:

Advertisements

Similar presentations

Introduction to Set Theory

Advertisements

Sets DISCRETE STRUCTURE ABDUL BASIT TAHIR, KAMRAN ALI, FAIZAN ILLAHI, NOMAN AHMAD, ARSALAN MUBASHIR.

Denoting the beginning

1 Section 1.7 Set Operations. 2 Union The union of 2 sets A and B is the set containing elements found either in A, or in B, or in both The denotation.

SET.   A set is a collection of elements.   Sets are usually denoted by capital letters A, B, Ω, etc.   Elements are usually denoted by lower case.

Chapter 5 Section 1 Sets Basics Set –Definition: Collection of objects –Specified by listing the elements of the set inside a pair of braces. –Denoted.

Chapter 2 Chapter The sample space of an experiment, denoted S , is the set of all possible outcomes of that experiment. An event is any collection.

1 Learning Objectives for Section 7.2 Sets After today’s lesson, you should be able to Identify and use set properties and set notation. Perform set operations.

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.

5.1 Sets Sets and Elements Union and Intersection Subset and Empty Set

This section will discuss the symbolism and concepts of set theory

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.

Venn Diagrams/Set Theory   Venn Diagram- A picture that illustrates the relationships between two or more sets { } are often used to denote members of.

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.

Introduction to Set Theory. Introduction to Sets – the basics A set is a collection of objects. Objects in the collection are called elements of the set.

Section 2.2 Subsets and Set Operations Math in Our World.

SECTION 2-3 Set Operations and Cartesian Products Slide

Sets Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Definition of Set A set is a collection of objects called elements.

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.

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

Basic Definitions of Set Theory Lecture 23 Section 5.1 Mon, Feb 21, 2005.

Set Operations Section 2.2.

Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 2.3 Venn Diagrams and Set Operations.

 Union Symbol ∪ If A and B are sets, their union is equal to all elements in both A & B A = {1,2,3,4} B = {2,4,5,6,7,8} A ∪ B = {1,2,3,4,5,6,7,8}

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.

Thinking Mathematically Venn Diagrams and Subsets.

Venn Diagrams and Sets. Venn Diagrams One way to represent or visualize sets is to use Venn diagrams:

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.

Set Notation 1.3 – 1.4 Quiz Topics

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.

6.1 Sets and Set Operations Day 2 Turn to page 276 and look at example 6.

A Π B = all elements in both sets A and B

Algebra 2 Chapter 12 Venn Diagrams, Permutations, and Combinations Lesson 12.2.

Sets and Operations TSWBAT apply Venn diagrams in problem solving; use roster and set-builder notation; find the complement of a set; apply the set operations.

Section 6.1 Set and Set Operations. Set: A set is a collection of objects/elements. Ex. A = {w, a, r, d} Sets are often named with capital letters. Order.

The set of whole numbers less than 7 is {1, 2, 3, 4, 5, 6}

Sets Finite 7-1.

CHAPTER 3 SETS, BOOLEAN ALGEBRA & LOGIC CIRCUITS

Unions and Intersections of Sets

Venn Diagrams and Set Operation

Lecture 04 Set Theory Profs. Koike and Yukita

Probability Using Venn Diagrams

Probability Vocabulary

The Basic Concepts of Set Theory

Counting and Probability Section 12.1: Sets and Counting IBTWW…

CSE 2353 – September 22nd 2003 Sets.

The Basic Concepts of Set Theory

Operations with Sets A = { 1, 2, 3 ,4, 5} B = { 2, 4, 6, 8, 10}

Session – 2 SETS & Operations of SETS

Chapter Sets &Venn Diagrams.

SETS Sets are denoted by Capital letters Sets use “curly” brackets

Thinking Mathematically

MATH 2311 Section 2.2.

CHAPTER 2 Set Theory.

Which sets are equal? Which sets are equivalent?

2.1 – Symbols and Terminology

Thinking Mathematically

7C Complements of Sets 7D-7G Venn Diagrams

Sets, Unions, Intersections, and Complements

MATH 2311 Section 2.2.

CHAPTER 2 Set Theory.

Presentation transcript:

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 of set B if every element that is in set A is also in set B. The notation for this is A  B. Set A is a proper subset of set B if every element that is in set A is also in set B and there is at least one element in set B that is not in set A. The notation for this is A  B.

Sets and Subsets If Set A contains all dogs, and Set B contains all Golden Retrievers, then B  A. However, A  B is not true.

An Example of Sets To belong to Set A, you must be over the age of 25. To belong to Set B, you must drive a blue car. Think about which sets you would belong to.

Set Union The union of A and B, which is written as c, is the set of all elements that belong either to set A or to set B (or that belong to both A and B). If you answered “yes” to either of the questions, you belong in the set union.

Set Intersection The intersection of A and B, which is written as A  B, is the set of all elements that belong to both to set A and set B. If the intersection of two sets is empty (the empty set is denoted by , then the sets are disjoint or mutually exclusive and we write A  B   If you answered, “yes” to both questions, you belong in set intersection.

Set Compliment The complement of set A, which is written as A c, is the set of all elements that are in the universal set but are not in set A. If you answered “no” to question A, you belong in the set compliment.

Examples: Use the following information to answer the questions: U   1, 2, 3, 4, 5, 6, 7, 8, 9, 10  A   1, 2, 5, 6, 9, 10  B   3, 4, 7, 8  C   2, 3, 8, 9, 10 

Venn Diagrams These are also known as “circle diagrams,” and they can be used to represent sets. Shade in A  B A  B A A B B

Venn Diagrams Shade in A c (A  B) c A A B B

Venn Diagrams Shade in A∩B∩C A∩C A B C A B C

Application Draw a Venn Diagram for the following situation: A group of 100 people are asked about their preference for soft drinks. The results are as follows: