Warm Up

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Warm Up
Lesson Presentation
Lesson Quiz
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Warm Up 1. 2. 3. 25
4. 6
Write all classifications that apply to each real
number.
rational, repeating decimal
irrational
rational, terminating decimal, integer, whole,
natural
rational, terminating decimal, integer
rational, terminating decimal
5.
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Sunshine State Standards
MA.912.D.7.1 Perform set operations such as union
and intersection, complement, and cross
product. Also MA.912.D.7.2, MA.912.A.10.1.
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Objectives
Perform operations involving sets. Use Venn
diagrams to analyze sets.
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Vocabulary
set
element union intersection empty
set universe complement subset cross product
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A set is a collection of items. An element is
an item in a set. You can use set notation to
represent a set by listing its elements between
brackets. The set F of riddles Flore has solved
is F 1, 2, 5, 6. The set L of riddles Leon
has solved is L 4, 5, 6.
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The intersection of two sets is a single set that
contains only the elements that are common to the
original sets. The notation F n L means the
intersection of sets F and L.
The empty set is the set containing no elements.
It is symbolized by ? or .
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Additional Example 1A Finding the Union and
Intersection of Sets
Find the union and intersection of each pair of
sets.
A 5, 10, 15 B 10, 11, 12, 13
To find the union, list every element that lies
in one set or the other.
A U B 5, 10, 11, 12, 13, 15
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Additional Example 1A Continued
Find the union and intersection of each pair of
sets.
A 5, 10, 15 B 10, 11, 12, 13
To find the intersection, list the elements
common to both sides.
A n B 10
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Additional Example 1B Finding the Union and
Intersection
Find the union and intersection of each pair of
sets.
A is the set of whole number factors of 15
B is the set of whole number factors of 25.
Write each set in set notation.
A U B 1, 3, 5, 15, 25
To find the union, list all of the elements in
either set.
To find the intersection, list the elements
common to both sets.
A n B 1, 5
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Check It Out! Example 1a
Find the union and intersection of each pair of
sets.
A 2, 1, 0, 1, 2 B 6, 4, 2, 0, 2, 4,
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A U B 6, 4, 2, 1, 0, 1, 2, 4, 6
To find the union, list all of the elements in
either set.
To find the intersection, list the elements
common to both sets.
A n B 2, 0, 2
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Check It Out! Example 1b
Find the union and intersection of each pair of
sets.
A is the set of whole numbers less than 10 B is
the set of whole numbers less than 8.
Write each set in set notation.
To find the union, list all of the elements in
either set.
A U B 0, 1, 2, 3,4, 5, 6, 7, 8, 9
To find the intersection, list the elements
common to both sets.
A n B 0, 1, 2, 3, 4, 5, 6, 7
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The universe, or universal set, for a particular
situation is the set that contains all of the
elements relating to the situation. The
complement of set A in universe U is the set of
all elements in U that are not in A.
In the contest described on slide 6, the universe
U is the set of all six riddles. The complement
of set L in universe U is the set of all riddles
that Leon has not solved.
Complement of L 1, 2, 3. Leon has not solved
riddles 1, 2, and 3.
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Additional Example 2A Finding the Complement of
a Set
Find the complement of set A in universe U.
U is the set of natural numbers less than 10 A
is the set of whole-number factors of 9.

A 1, 3 ,9 U 1, 2, 3, 4, 5, 6, 7, 8, 9
Draw a Venn diagram to show the complement of set
A in universe U
Complement of A 2, 4, 5, 6, 7, 8
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Additional Example 2B Finding the Complement of
a Set
Find the complement of set A in universe U.
U is the set of rational numbers A is the set
of terminating decimals.
Complement of A the set of repeating decimals.
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Reading Math
Finite sets have finitely many elements, as in
Example 2A. Infinite sets have infinitely many
elements, as in Example 2B.
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Check It Out! Example 2
Find the complement of set A in universe U. U
is the set of whole numbers less than 12 A is
the set of prime numbers less than 12.
0, 1, 4, 6, 8, 9, 10
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Additional Example 3 Determining
Relationships Between Sets
A is the set of positive multiples of 3, and B is
the set of positive multiples of 9. Determine
whether the statement A ? B is true or false. Use
a Venn diagram to support your answer.
Draw a Venn diagram to show these sets.
False B ? A
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Check It Out! Example 3
A is the set of whole-number factors of 8, and B
is the set of whole-number factors of 12.
Determine whether the statement A ? B B is true
or false. Use a Venn diagram to support your
answer.
False the element 8 of set A, is not an
element of set B.
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The cross product (or Cartesian product) of two
sets A and B, represented by A ? B, is a set
whose elements are ordered pairs of the form (a,
b), where a is an element of A and b is an
element of B. You can use a chart to find A ? B.
Suppose A 1, 2 and B 40, 50, 60.
A ? B (1, 40), (1, 50), (1, 60), (2, 40), (2,
50), (2, 60)
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Additional Example 4 Application
The set C S, M, L represents the sizes of
cups (small, medium, and large) sold at a frozen
yogurt shop. The set F V, B, P represents the
available flavors (vanilla, banana, peach). Find
the cross product C ? F to determine all of the
possible combinations of sizes and flavors.
Make a chart to find the cross product. Each pair
represents one combination of flavors and sizes.
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Check It Out! Example 4
The set MN M, N, MN represents the blood
groups in the MN system. Find ABO MN to
determine all of possible blood groups in the ABO
MN systems.
Make a chart to find the cross product. Each pair
represents one combination of ABO and MN blood
groups.
ABO ? MN (A, M), (A, N), (A, MN), (B, M),(B,
N), (B, MN), (AB, M), (AB, N), (AB, MN), (O, M),
(O, N), (O, MN) 12 possible blood groups.
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Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
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Lesson Quiz Part I
1. Find the union and intersection of sets A and
B. A 4, 5, 6 B 5, 6, 7, 8
A U B 4, 5, 6, 7, 8 A n B 5, 6
2. Find the complement of set C in universe U.
U is the set of whole numbers less than 10 C
0, 2, 5, 6.
1, 3, 4, 7, 8, 9
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Lesson Quiz Part II
D is the set of whole-number factors of 8, and E
is the set of whole-number factors of 24.
Determine whether the statement D ? E is true or
false. Use a Venn diagram to support your answer.
3.
true
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Lesson Quiz Part III
F ? G (1, 2), (1, 0), (1, 2), (0, 2),
(0, 0), (0, 2), (1, 2), (1, 0), (1, 2)
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Lesson Quiz for Student Response Systems
1. A set is defined as
A. a collection of items
B. a collection of elements
C. a union of items
D. a union of elements
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Lesson Quiz for Student Response Systems
2. The symbol ? means
A. intersection
B. union
C. empty set
D. set notation
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Lesson Quiz for Student Response Systems
3. The intersection
A. contains common elements
B. is the empty set
C. contains the union
D. contains uncommon elements
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Lesson Quiz for Student Response Systems
4. Find the intersection of the two sets.
A. A ? B 1, 3, 4, 5, 6, 7
B. A ? B 2
C. A ? B 2
D. A ? B 1, 3, 4, 5, 6, 7
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Lesson Quiz for Student Response Systems
5. Find the compliment of set A in universe U.
U All whole-numbers less than 9
A All even numbers
A. 2, 4, 6, 8
B. 1, 3, 6, 7, 8
C. 1, 3, 5, 7, 9
D. 1, 3, 5, 7