Transcript sets_and_set_operati..

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
proper/improper subset
intersection of sets
union of sets
mutually exclusive
complement of a set
Set:
roster notation:
set builder notation:
well defined set:
Determine if the given set is well
defined.
The set of all pink automobiles
The set of all good bands
The set of odd numbers
The set of small numbers
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
complement

not (in)
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).
•Find the set A  B.
•Find the set B .
•Find the set A  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:
•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.
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 illustration 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.