Transcript A B - VincentPienaar

12-8 Set Theory
Warm Up
Problem of the Day
Lesson Presentation
Course 2
12-8 Set Theory
Warm Up
Tell in which intervals of x the graph shows
constant rates of change.
from x = 0 to x = 2, x =2 to x = 4, x = 4 to x = 5,
and x = 5 to x = 9
Course 2
12-8 Set Theory
Problem of the Day
What is the intersection of the set of all
prime numbers and the set of all even
numbers?
2
Course 2
12-8 Set Theory
Learn to use set notation and to identify
relationships between sets.
Course 2
12-8 Set
Insert
Lesson Title Here
Theory
Vocabulary
set
element
Course 2
12-8 Set Theory
The states that are bordered by the Pacific Ocean
for a set. The set of states in the United States
that are bordered by the Pacific Ocean includes
California, Oregon, Washington, Alaska, and
Hawaii.
A set is a collection of objects. Each object in a
set is an element of the set. The special set that
contains no elements is the null set, or empty
set. When describing sets using symbols, you
can use either roster notation or set-builder
notation.
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12-8 Set Theory
{CA, OR, WA, AK, HI}
Roster notation lists
all of the elements.
{x|x is a state that is
bordered by the Pacific
Ocean}
Set-builder notation
gives a rule.
Reading Math
Read the notation {x|x is a real number} as
“the set of all x such that x is a real number.”
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12-8 Set Theory
Additional Example 1: Writing in Set Notation
Write each set using roster notation or set
builder notation.
A. the set of all positive multiples of 3 less than or
equal to 15
The numbers can be
{3, 6, 9, 12, 15} listed conveniently. Use
roster notation.
B. the set of all multiples of 3
{x|x is a multiple of 3} The numbers follow a
rule but cannot all be
listed conveniently.
Use set-builder notation.
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12-8 Insert
Lesson Title Here
Set Theory
Try This: Example 1
Write each set using roster notation or set
builder notation.
A. the set of all odd numbers from 1 to 10,
including 1
The numbers can be listed
{1, 3, 5, 7, 9} conveniently. Use roster
notation.
B. the set of all odd integers greater than zero
The numbers follow a rule
{x|x is an odd
but cannot all be listed
counting number}
conveniently. Use set-builder
notation.
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12-8 Set Theory
The following notations show how different sets
can relate to each other.
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12-8 Set Theory
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12-8 Set Theory
Course 2
12-8 Set Theory
Additional Example 2A: Identifying Relationships
Between Sets
Find A B and A  B. Tell whether A  B,
B  A, or neither.
A. A = {0, 5, 10}; B = {1, 2, 3, 4, 5}
A  B = {5}
5 is in both A and B.
A  B = {0, 1, 2, 3, 4, 5, 10} List the members of
both sets.
Neither set is a subset of the other.
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12-8 Set Theory
Additional Example 2B: Identifying Relationships
Between Sets
Find A  B and A  B. Tell whether A  B,
B  A, or neither.
B. A = {1, 2, 3}; B = {1, 2, 3, 4, 5}
A  B = {1, 2, 3}
1, 2, and 3 in both A
and B.
A  B = {1, 2, 3, 4, 5}
List the members of
both sets.
AB
All the members of A
are in B.
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12-8 Set Theory
Additional Example 2C: Identifying Relationships
Between Sets
Find A  B and A  B. Tell whether A  B,
B  A, or neither.
C. A = {x|x is an even integer};
B = {x|x is an odd integer}
No number is both
AB={}=Ø
even and odd.
Together, the set of
A  B = {x|x is an integer} even integers and the
set of odd integers
make up the set of
integers.
Neither set is a subset of the other.
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12-8 Set Theory
Try This: Example 2A
Find A B and A  B. Tell whether A  B,
B  A, or neither.
A. A = {0, 1, 2}; B = {2, 3, 4, 5}
A  B = {2}
A  B = {0, 1, 2, 3, 4, 5}
2 is in both A and B.
List the members of
both sets.
Neither set is a subset of the other.
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12-8 Set Theory
Try This: Example 2B
Find A  B and A  B. Tell whether A  B,
B  A, or neither.
B. A = {4, 5}; B = {1, 2, 3, 4, 5, 6}
A  B = {4, 5}
4 and 5 are in both
A and B.
A  B = {1, 2, 3, 4, 5, 6}
List the members of
both sets.
AB
All the members of A
are in B.
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12-8 Set Theory
Additional Example 2C: Identifying Relationships
Between Sets
Find A  B and A  B. Tell whether A  B,
B  A, or neither.
C. A = {x|x is an even integer};
B = {x|x is an irrational number}
No number is both
AB={}=Ø
an integer and
irrational.
List the members of
A  B = {x|x is an even
both sets.
integer or an irrational
number}
Neither set is a subset of the other.
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12-8 Set
Insert
Theory
Lesson Title Here
Lesson Quiz: Part 1
Write each set using roster notation or setbuilder notation.
1. The set of positive multiples of 4 less than 24
{4, 8, 12, 16, 20}
2. The set of all state capitals.
{x|x is the capital of a state}
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12-8 Set
Insert
Theory
Lesson Title Here
Lesson Quiz: Part 2
Find A  B and A  B and tell whether one set is
a subset of the other.
3. A = {–8, –10, –12, –14} and
B = {–8, –12, –16}
A  B = {–8, –10, –12, –14, –16}
A  B = {–8, –12}; neither is a subset of the other.
2. A = {whole numbers} and
B = {3, 5, 7, 9, 12}
A  B = {whole numbers}
A  B = {3, 5, 7, 9, 12}; B  A
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