Download aps08_ppt_0201

AND
Copyright © 2009 Pearson Education, Inc.
Chapter 2 Section 1 - Slide 1
Chapter 2
Sets
Copyright © 2009 Pearson Education, Inc.
Chapter 2 Section 1 - Slide 2
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 3
Section 1
Set Concepts
Copyright © 2009 Pearson Education, Inc.
Chapter 2 Section 1 - Slide 4
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.”
Copyright © 2009 Pearson Education, Inc.
Chapter 2 Section 1 - Slide 5
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.
Copyright © 2009 Pearson Education, Inc.
Chapter 2 Section 1 - Slide 6
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.
Copyright © 2009 Pearson Education, Inc.
Chapter 2 Section 1 - Slide 7
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 setbuilder 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.
Copyright © 2009 Pearson Education, Inc.
Chapter 2 Section 1 - Slide 8
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.

Copyright © 2009 Pearson Education, Inc.
Chapter 2 Section 1 - Slide 9
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.
Copyright © 2009 Pearson Education, Inc.
Chapter 2 Section 1 - Slide 10
Equal Sets

Equal sets have the exact same elements in
them, regardless of their order.

Symbol:

Example: { 1, 5, 7 } = { 5, 7, 1 }
A=B
Copyright © 2009 Pearson Education, Inc.
Chapter 2 Section 1 - Slide 11
Cardinal Number

The number of elements in set A is its cardinal
number.

Symbol: n(A)

Example:
Copyright © 2009 Pearson Education, Inc.
A = { 1, 5, 7, 10 }
n(A) = 4
Chapter 2 Section 1 - Slide 12
Equivalent Sets

Equivalent sets have the same number of
elements in them.

Symbol: n(A) = n(B)

Example:
Copyright © 2009 Pearson Education, Inc.
A = { 1, 5, 7 } , B = { 2, 3, 4 }
n(A) = n(B) = 3
So A is equivalent to B.
Chapter 2 Section 1 - Slide 13
Empty (or Null) Set

The null set (or empty set ) contains absolutely
NO elements.

Symbol:
 or
Copyright © 2009 Pearson Education, Inc.
 
Chapter 2 Section 1 - Slide 14
Universal Set

The universal set contains all of the possible
elements which could be discussed in a
particular problem.

Symbol: U
Copyright © 2009 Pearson Education, Inc.
Chapter 2 Section 1 - Slide 15