Ch 9 Inequalities and Absolute
Value
9.1 Sets, Intersection and Unions
Goal(s): 1.) Name sets using set- builder and
roster notation
2.) Find Intersections and Unions of
sets
“Set” is a well-defined collection of
objects called “members” or “elements”
Wearing
sweatshirt
Blue eyes
“Roster Notation”
• The set of all whole numbers greater than
20 can be written: {21, 22, 23, 24, …}
Use pointed
brackets
List each
element
Three dots, called an ellipsis, indicate that
the pattern continues forever, following
the pattern set by the first 4 numbers.
Write using “roster notation”
The set of all integers greater than 5
and less than or equal to 10
{6,7,8,9,10}
Write using “roster notation”
The set of all prime numbers
less than 12
{2,3,5,7,11}
Write using “roster notation”
The set of all positive odd numbers
{1,3,5,7,…}
List the first 4
Then write the ellipsis to show
“the pattern continues”
Write using “roster notation”
The set of all positive multiples of 3
{3,6,9,12,…}
Set-builder Notation
• Used to describe HOW a set is built, for
example
• {x|x is a whole number and x > 20}
Description
Means “such that”
Write using “set-builder notation”
The set of all integers greater than 7
{x|x is an integer and
x > 7}
Write using “set-builder notation”
The set of all multiples of 5 that are
less than 24
{x|x is a multiple of 5
and x < 24}
Use capital letters to name sets
• “Z” is used to name the set of all integers
• “Q” used for the set of all rational numbers
€means “is an element of”
And
€ means “is not an element of”
Let E be the set of even numbers
True or False ?
18 € E
Let E be the set of even numbers
True or False ?
12 € E
Write using “roster notation”
and “set builder notation”:
The set G of whole numbers greater than 5
G = {6,7,8,9,…}
G = {x|x is a whole number
and x>5}
Write using “roster notation”
and “set builder notation”:
The set T of multiples of 5 less than 24
T = {20,15,10,5,0,-5,…}
T = {x|x is a multiple of 5 and
x < 24
Intersection of two sets
• Is the set of all members common to
both sets.
• Written A B (“A intersection B”)
• Venn diagram representation:
A
B
A = {1,2,3,4,5,6}
B = {-2,-1,0,1,2,3}
Find A  B.
4
5
6
1
A
2
3
-2
B
-1
0
T = {0,1,6,9}
P = {-3,-2,0,1,5}
S = {-3,1,6}
Find T  P.
6
9T
0
1
-3
P
-2
5
T = {x|x is an even number}
P = {y|y is an odd number}
Find T  P.
TP 
Intersection is the" emptyset"
Union of two sets
• Is the set of all members either or both
sets.
• Written AB (“A union B”)
• Venn diagram representation:
A
B
Union of two sets
• Is the set of all members either or both
sets.
• Written AB (“A union B”)
• Venn diagram representation:
A
B
A = {1,2,3,4,5,6}
B = {-2,-1,0,1,2,3}
Find A  B.
A  B  {-2,-1,0,1,2,3,4,5,6}
4
5
6
1
A
2
3
-2
B
-1
0
6 A
6 B
3 A  B
Assignment:
Page 403
(2-42) even