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

AND

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

Chapter 2

Sets

Copyright © 2009 Pearson Education, Inc. Chapter 2 Section 1 - 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 1 - Slide 4

Section 1

Set Concepts

Chapter 2 Section 1 - Slide 5Copyright © 2009 Pearson Education, Inc.

Set

A collection of objects, which are called elements or members of the set.

Listing the elements of a set inside a pair of braces, { }, is called roster form.

The symbol , read “is an element of,” is used to indicate membership in a set.

The symbol means “is not an element of.”

Chapter 2 Section 1 - Slide 6Copyright © 2009 Pearson Education, Inc.

Well-defined Set

A set which has no question about what elements should be included.

Its elements can be clearly determined. No opinion is associated its the members.

Chapter 2 Section 1 - Slide 7Copyright © 2009 Pearson Education, Inc.

Roster Form

This is the form of the set where the elements are all listed, separated by commas.

Example: Set A is the set of all natural numbers less than or equal to 25.

Solution: A = {1, 2, 3, 4, 5,…, 25} The 25 after the ellipsis indicates that the elements continue up to and including the number 25.

Chapter 2 Section 1 - Slide 8Copyright © 2009 Pearson Education, Inc.

Set-Builder (or Set-Generator) Notation

A formal statement that describes the members of a set is written between the braces.

A variable may represent any one of the members of the set.

Example: Write set B = {2, 4, 6, 8, 10} in set-builder notation.

Solution:

B x x N and x is an even number 10 .

The set of all x such that x is a natural number and x is an even number 10.£

Chapter 2 Section 1 - Slide 9Copyright © 2009 Pearson Education, Inc.

Finite Set

A set that contains no elements or the number of elements in the set is a natural number.

Example:

Set S = {2, 3, 4, 5, 6, 7} is a finite set because the number of elements in the set is 6, and 6 is a natural number.

Chapter 2 Section 1 - Slide 10Copyright © 2009 Pearson Education, Inc.

Infinite Set

An infinite set is a set where the number of elements is not or a natural number; that is, you cannot count the number of elements.

The set of natural numbers is an example of an infinite set because it continues to increase forever without stopping, making it impossible to count its members.

Chapter 2 Section 1 - Slide 11Copyright © 2009 Pearson Education, Inc.

Equal sets have the exact same elements in them, regardless of their order.

Symbol: A = B

Example: { 1, 5, 7 } = { 5, 7, 1 }

Equal Sets

Chapter 2 Section 1 - Slide 12Copyright © 2009 Pearson Education, Inc.

Cardinal Number

The number of elements in set A is its cardinal number.

Symbol: n(A)

Example: A = { 1, 5, 7, 10 }

n(A) = 4

Chapter 2 Section 1 - Slide 13Copyright © 2009 Pearson Education, Inc.

Equivalent Sets

Equivalent sets have the same number of elements in them.

Symbol: n(A) = n(B)

Example: A = { 1, 5, 7 } , B = { 2, 3, 4 }

n(A) = n(B) = 3

So A is equivalent to B.

Chapter 2 Section 1 - Slide 14Copyright © 2009 Pearson Education, Inc.

Empty (or Null) Set

The null set (or empty set ) contains absolutely NO elements.

Symbol: or

Chapter 2 Section 1 - Slide 15Copyright © 2009 Pearson Education, Inc.

Universal Set

The universal set contains all of the possible elements which could be discussed in a particular problem.

Symbol: U