# holt set theory

Document Sample

```					1-6 Set Theory

Warm Up
Lesson Presentation
Lesson Quiz
1-6 Set Theory
Warm Up
Write all classifications that apply to each real
number.
5
1.      rational, repeating decimal
9
2. 5    irrational

rational, terminating decimal, integer,
3. 25
whole, natural

4. –6    rational, terminating decimal, integer
7    rational, terminating decimal
5.
10
1-6 Set Theory

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.
1-6 Set Theory

Objectives
Perform operations involving sets.
Use Venn diagrams to analyze sets.
1-6 Set Theory

Vocabulary
set
element
union
intersection
empty set
universe
complement
subset
cross product
1-6 Set Theory
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}.
The union of two sets is a single set of all the
elements of the original sets. The notation F L means
the union of sets F and L.

Union          F L = {1, 2, 4, 5, 6}
3   Together, Flore and Leon
Set F      Set L       have solved riddles 1, 2,
1 2 56       4         4, 5, and 6.
1-6 Set Theory

The intersection of two sets is a single set that
contains only the elements that are common to the
original sets. The notation F ∩ L means the
intersection of sets F and L.

Intersection       F ∩ L = {5, 6}
3   Flore and Leon have both
set F     set L       solved riddles 5 and 6.
1 2 56      4

The empty set is the set containing no elements. It
is symbolized by  or {}.
1-6 Set Theory

Writing Math
In set notation, the elements of a set can be
written in any order, but numerical sets are
usually listed from least to greatest without
repeating any elements.
1-6 Set Theory
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}

Set A   Set B
5    15 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}
1-6 Set Theory

Find the union and intersection of each pair of
sets.
A = {5, 10, 15}; B = {10, 11, 12, 13}

Set A   Set B
5    15 10 11
12 13

To find the intersection, list the elements
common to both sides.
A ∩ B = {10}
1-6 Set Theory
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.
A = {1, 3, 5, 15}            Write each set in set
B = {1, 5, 25}               notation.
A U B = {1, 3, 5, 15, 25} To find the union, list all of
the elements in either set.
A ∩ B = {1, 5}            To find the intersection, list
the elements common to
both sets.
1-6 Set Theory
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, 6}

A U B = {–6, –4, –2, –1, 0, 1, 2, 4, 6}
To find the union, list all of
the elements in either set.

A ∩ B = {–2, 0, 2}                   To find the intersection, list
the elements common to
both sets.
1-6 Set Theory
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.
A = {1, 2, 3, 4, 5, 6, 7, 8, 9}      Write each set in set
B = {1, 2, 3, 4, 5, 6, 7}            notation.

A U B = {0, 1, 2, 3,4, 5, 6,        To find the union, list all of
7, 8, 9}                   the elements in either set.

A ∩ B = {0, 1, 2, 3, 4, 5, 6, 7} To find the intersection, list
the elements common to
both sets.
1-6 Set Theory

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.
Complement of L
In the contest described on       Universe U           3
slide 6, the universe U is
Set F       Set L
the set of all six riddles. The      1 2 56       4
complement of set L in
universe U is the set of all
riddles that Leon has not Complement of L = {1, 2, 3}.
solved.                      Leon has not solved riddles 1,
2, and 3.
1-6 Set Theory
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     Universe U          8
show the complement of                     2       7
set A in universe U            Set A
1    3 9             4
Complement of A = {2,                            5 6
4, 5, 6, 7, 8}
1-6 Set Theory

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.
1-6 Set Theory

Finite sets have finitely many elements, as in
Example 2A. Infinite sets have infinitely many
elements, as in Example 2B.
1-6 Set Theory
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}
1-6 Set Theory

One set may be entirely contained within another
set. Set B is a subset of set A if every element of
set B is an element of set A. The notation B  A
means that set B is a subset of set A.
1-6 Set Theory
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.

Draw a Venn diagram
to show these sets.
Set B
Set A multiples
multiples of 3 that are
False; B  A                   of 9      not multiples of
9
1-6 Set Theory
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

False; the element 8 of
set A, is not an element       Set A     Set B
of set B.                              1 3
8
42    6
12
1-6 Set Theory

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}.               Set B
40     50     60
1    (1,40) (1,50) (1,60)
Set A
2     (2,40) (2,50) (2,60)

A  B = {(1, 40), (1, 50), (1, 60), (2, 40),
(2, 50), (2, 60)}
1-6 Set Theory
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.                     Set C
C  F a chart to find the cross
Make =                                S     M     L
{(S, V), (S, B), (S, P),
product.
(M, V), (M,B), (M, P),            V   (S,V) (M,V) (L,V)
Each pair represents one Set F
(L,V), (L, B), (L, P)};           B   (S,B) (M,B) (L,B)
combination of flavors and
9 possible combinations               (S,P) (M,P) (L,P)
sizes.                           P
1-6 Set Theory
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.                   M      N     MN

Make a chart to find   A (A, M) (A, N) (A, MN)
the cross product.     B (B, M) (B, N) (B, MN)
Each pair represents
one combination of    AB (AB,M) (AB,N) (AB,MN)
ABO and MN blood
groups.                O (O, M) (O, N) (O, M)
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.
1-6 Set Theory

Lesson Quizzes

Standard Lesson Quiz

Lesson Quiz for Student Response Systems
1-6 Set Theory

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 ∩ 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}
1-6 Set Theory

Lesson Quiz: Part II

3. 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
true
Set E        6
Set D
2    4      3
8   1            12
24
1-6 Set Theory

Lesson Quiz: Part III
4. Find the cross product F  G.
F = {–1, 0, 1}; G = {–2, 0, 2}

F  G = {(–1, –2), (–1, 0), (–1, –2), (0, –2),
(0, 0), (0, 2), (1, –2), (1, 0), (1, 2)}
1-6 Set Theory

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
1-6 Set Theory

Lesson Quiz for Student Response Systems

2. The symbol  means:

A. intersection
B. union
C. empty set
D. set notation
1-6 Set Theory

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
1-6 Set Theory

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}                   Set A        Set B
8           3
C. A  B = {2}                  4         2        6
1           12
D. A  B = {1, 3, 4, 5, 6, 7}
1-6 Set Theory

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}

```
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
 views: 0 posted: 5/7/2013 language: English pages: 33
gegouzhen12