Section 1.3 The Language of Sets. Objective 1.Use three methods to represent sets. 2.Define and recognize the empty set. 3.Use the symbols and. 4.Apply.

Slides:



Advertisements
Similar presentations
 A set is a collection of objects. Each object in the set is called an element or member of the set. Example. Let A be a collection of three markers.
Advertisements

Slide 2-1 Copyright © 2005 Pearson Education, Inc. SEVENTH EDITION and EXPANDED SEVENTH EDITION.
Chapter 2 The Basic Concepts of Set Theory
Set Theory.
Ch 9 Inequalities and Absolute Value
Chapter 2 The Basic Concepts of Set Theory © 2008 Pearson Addison-Wesley. All rights reserved.
2.1 – Symbols and Terminology Definitions: Set: A collection of objects. Elements: The objects that belong to the set. Set Designations (3 types): Word.
SET Miss.Namthip Meemag Wattanothaipayap School. Definition of Set Set is a collection of objects, things or symbols. There is no precise definition for.
Sets Chapter 2 1.
Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 2.1 Set Concepts
Partially borrowed from Florida State University
Objectives: By the end of class, I will be able to:  Identify sets  Understand subsets, intersections, unions, empty sets, finite and infinite sets,
Any well-defined collection of objects and each object of the collection is an element or member of the set.
Understanding Set Notation
Section 2.1 Basic Set Concepts
© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 2 Set Theory.
Course: Math Literacy Aim: Set Notation Aim: How do we deal with chaos? Do Now: How many of you drive yourself to school? How many of you take the bus.
The Language of Sets MATH 102 Contemporary Math S. Rook.
SET THEORY. BASIC CONCEPTS IN SET THEORY Definition: A set is a collection of well-defined objects, called elements Examples: The following are examples.
Section 1.4 Comparing Sets.
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 2.1, Slide 1 CHAPTER 2 Set Theory.
2.1 Sets and Whole Numbers Remember to Silence Your Cell Phone and Put It In Your Bag!
Set Theory Symbols and Terminology Set – A collection of objects.
Thinking Mathematically Chapter 2 Set Theory 2.1 Basic Set Concepts.
Slide Chapter 2 Sets. Slide Set Concepts.
Chapter 2 Section 1 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.
2.1 Symbols and Terminology. Designating Sets A set is a collection of objects (in math, usually numbers). The objects belonging to the set are called.
Slide Section 2-1 Symbols and Terminology. SYMBOLS AND TERMINOLOGY Designating Sets Sets of Numbers and Cardinality Finite and Infinite Sets Equality.
Unit 2 Sets.
Copyright © 2010 Pearson Education, Inc. All rights reserved Sec
ELEMENTARY SET THEORY.
Module Code MA1032N: Logic Lecture for Week Autumn.
Section 2.1 Set Concepts.
Section 1Chapter 1. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Basic Concepts Write sets using set notation. Use number.
 A set is a collection of objects. Each object in the set is called an element or member of the set. Example. Let A be a collection of three markers.
Chapter 1 Section 1 - Slide 1 Copyright © 2009 Pearson Education, Inc. AND.
 Homework Answers Standardized Test Prep & Mixed Review P. 192 #s all 58)62) 59)63) 60) 64) 61) 65)
 Objectives: To write sets and identify subsets To find the complement of a set Section 3 – 5 Working With Sets.
Fr: Discrete Mathematics by Washburn, Marlowe, and Ryan.
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.
Thinking Mathematically Basic Set Concepts. A “set” is a collection of objects. Each object is called an “element” of the set. Often the objects in a.
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.
Set Builder Notation. If you recall, a set is a collection of objects which we write using brackets and name using a capital letter. Remember also that:
Copyright © 2015, 2011, 2007 Pearson Education, Inc. Section 2.2, Slide 1 CHAPTER 2 Set Theory.
Math in Our World Section 2.1 The Nature of Sets.
Sets Page 746.
Chapter 2: SETS.
Lesson 2.1 Basic Set Concepts.
The Basic Concepts of Set Theory
Ch. 2 – Set Theory 2.1 Notes Basic Set Concepts.
CS100: Discrete structures
        { } Sets and Venn Diagrams Prime Numbers Even Numbers
The Basic Concepts of Set Theory
Chapter 1 Section 1.
Chapter 2 The Basic Concepts of Set Theory
Section 2.1 Basic Set Concepts
Chapter 2 The Basic Concepts of Set Theory
CHAPTER 2 Set Theory.
Thinking Mathematically
CHAPTER 2 Set Theory.
2.1 – Symbols and Terminology
CHAPTER 2 Set Theory.
Section 2.1 Set Concepts.
2.1 Basic Set Concepts.
Section 2.1 Set Concepts.
§2.1 Basic Set Concepts.
CHAPTER 2 Set Theory.
Thinking Mathematically
Section 2.1 Set Concepts.
Presentation transcript:

Section 1.3 The Language of Sets

Objective 1.Use three methods to represent sets. 2.Define and recognize the empty set. 3.Use the symbols and. 4.Apply set notation to sets of natural numbers. 5.Determine a set’s cardinal number. 6.Distinguish between finite and infinite sets.

Key Terms Set: a collection of objects. Elements/Members: the individual objects in the collection. Well-Defined: the set contents can be clearly defined. Naming Sets: sets normally denoted by a capital letter. Lower-case letters are used to denote elements in a set.

Three Methods used to Designate Sets 1.Word Description: describe the set using words. 2.Roster Form: set of elements listed inside a pair of braces { } separated by commas. i.Braces are important because they indicate a set. Never use parenthesis ( ), or brackets [ ]. ii.Ellipses: three dots after the last element in a set, indicates the set continues in the same manner up to the last element or to infinity. 3.Set-Builder Notation: also called set-generator notation. i.A = {x/condition(s)}…This is read as “The set A is the set of all elements x such that certain conditions are met”.

Example 1: Word Description {Saturday, Sunday} {April, August} ▫NOTE: when writing sets of numbers, be careful of the words “between” and “inclusive”.  Inclusive means all numbers are included; between does not. {9, 10, 11, 12,…,25}

Example 2: Roster Form The set of the months that have exactly 30 days. The set of U. S. coins that have a value less than a dollar.

Example 3: Set-Builder Notation C is the set of all x such that x is a carnivorous animal. The set of natural numbers less than or equal to 6.

Example 4: and The symbol,, is read “is an element of” and indicates membership in a set. The symbol,, is read “is not an element of” and indicates object not an element of the set. Determine whether each statement is true or false. a.r {a, b, c,…,z} b.7 {1, 2, 3, 4, 5} c.{a} {a, b}

Natural Numbers The set of counting numbers, starting with 1 and going to infinity is called the “Natural Numbers”. ▫Natural numbers are represented by a bold face N.

Example 5: Natural Numbers Express each of the following sets using roster method. a.Set A is the set of natural numbers less than 5. b.Set B is the set of natural numbers greater than or equal to 25. c.E = {x/x N and x is even}

Example 6: Express each of the following sets using the roster method. a.{x/x N and x < 100} b.{x/x N and 70 < x < 100}

Example 7: Empty Set Empty Set: also called the null set, is the set that contains no elements. The empty set is represented by { } or ø. ▫The empty set is not represented by {ø}. This represents the set containing the element ø. Which of the following is the empty set. a.{x/x is a number less than 3 or greater than 5} b.{x/x is a number less than 3 and greater than 5}

Example 8: Well-Defined Well-Defined: the set contents can be clearly defined. The set of the days of the week. The set of the three best songs.

Example 9: Cardinality Cardinal Number: the number of elements in a set, also called cardinality. ▫Represented by the symbol n(A). Find the cardinal number of each of the following sets: a.A = {7, 9, 11, 13} b.B = {0} c.C = {13, 14, 15,…,22, 23}

Example 10: Finite and Infinite Sets A set is finite if it contains no elements or n(A) is a natural number. A set whose cardinality is not zero or a natural number is called an infinite set. {1, 4, 7,...,16} {x/x is a N > 58}

Section 1.3 Assignments Classwork: ▫Textbook pg. 28/2, 4…Set-builder Notation 6, 8…Roster Form 10, 12…Word Description 30 – 64 Even  Must write problems and show ALL work to receive credit for the assignment. Homework: