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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”
Blue eyesWearing sweatshirt
“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}
Means “such that”
Description
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}
B.A Find
1
2
3
A
4
5
6
B
-2
-1
0
T = {0,1,6,9}P = {-3,-2,0,1,5}S = {-3,1,6}
P.T Find
0
1T6
9 P
-3
-2
5
T = {x|x is an even number}P = {y|y is an odd number}
P.T Find
set"empty " theis onIntersecti
PT
Union of two sets
• Is the set of all members either or both sets.
• Written AB (“A union B”)• Venn diagram representation:
A B
Union of two sets
• Is the set of all members either or both sets.
• Written AB (“A union B”)• Venn diagram representation:
A B
A = {1,2,3,4,5,6}B = {-2,-1,0,1,2,3}
B.A Find
1
2
3
A
4
5
6
B
-2
-1
0
},2,3,4,5,6{-2,-1,0,1BA
A6B6
BA3
Assignment:
Page 403(2-42) even