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