Transcript sets_and_set_operati.. - Arizona State University

MAT 142
Lecture Video Series
Sets and Set Operations
Objectives
• Determine if a set is well defined.
• Write all the subsets of a given set and
label the subsets as proper or improper.
• Given a universal set and some subsets,
find a complement, intersection or
union.
• Draw a Venn diagram to illustrate two
sets.
• Use the cardinal number formula.
Vocabulary
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roster notation
set-builder notation
well defined set
cardinal number
empty set
subset
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proper/improper subset
intersection of sets
union of sets
mutually exclusive
complement of a set
Set Vocabulary:
roster notation:
a complete or implied listing of
all the elements of the set
set builder notation:
used when the roster method is
cumbersome or impossible
Set Vocabulary:
well defined set:
A set is well-defined if any given
object either is an element of the
set, or is not an element of the set
Determine if the given set is well
defined.
The set of all good bands
The set of odd numbers
- not well defined
- well defined
The set of small numbers
- not well defined
Symbols related to sets:
Symbol
Term
 or { }
empty set

in

not in
n(A)
number
Symbols related to sets:
Term
Symbol
Read as
union

or
intersection

and
A
not (in A)
complement
subset

Given the sets
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
A = {0, 2, 4, 5, 6, 8}, and
B = {1, 3, 5, 7}
Answer the questions below:
•Find n(B). n(B) = 4
•Find the set A  B.
•Find
A  B = {5}
These are the things that are in set A and also
in set
B at
{0, 2, 4, 6, 8, 9}
the
set
B the sameB =time.
These are the things that are in set U (the
universe for our problem) that are not in set B.
Given the sets
U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
A = {0, 2, 4, 5, 6, 8}, and
B = {1, 3, 5, 7}
Answer the questions below:
•Find the set A  B .
•Is 7A true or false?
•Is 5B true or false?
Formulas
Cardinal Number Formula for the Union of
Sets
n(AB) = n(A) + n(B) — n(AB)
Cardinal Number Formula for the
Complement of a Set
n (U )  n (A)  n (A)
Suppose n(U) = 61, n(A) = 32, and
n(B) = 26.
If n(AB) = 40, find n(AB) and draw
a Venn diagram to illustrate the
composition of U.
n(AB) = n(A) + n(B) — n(AB)
In a recent health survey, 750 single men in
their twenties were asked to check the
appropriate box or boxes on the following form.
I am a member of a private gym.
I am a vegetarian.
The results were tabulated as follows:
374 checked the gym box
92 checked the vegetarian box
332 were blank (no boxes checked)
750 men surveyed
374 checked the gym box
92 checked the vegetarian box
332 were blank (no boxes checked)
1. Draw a Venn diagram illustrating the results
of the survey.
2. What percent of these men were both
members of a private gym and vegetarians.
Cards
Cards
Determine how many cards, in an ordinary
deck of 52, are clubs or twos.
Cards
Determine how many cards, in an ordinary
deck of 52, are face cards or diamonds.
Cards
Determine how many cards, in an ordinary
deck of 52, are threes or sixes.
Cards
Determine how many cards, in an ordinary
deck of 52, are threes and sixes.
Elizabeth Jones
for
The School of Mathematical and Statistical
Sciences
at
Arizona State University
Videographer
Mike Jones