Sets and Set Operations. Objectives Determine if a set is well defined. Write all the subsets of a...
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![Page 1: 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.](https://reader035.fdocuments.in/reader035/viewer/2022062407/56649f585503460f94c7d08e/html5/thumbnails/1.jpg)
Sets and Set Operations
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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.
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Vocabulary
• 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
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Set:
roster notation:
set builder notation:
well defined set:
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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
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Symbols related to sets:
Symbol Term
or { } empty set
in
not in
n(A) number
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Symbols related to sets:
Term Symbol Read as
union or
intersection and
complement not (in A)
subset A
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Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},A = {0, 2, 4, 5, 6, 8}, andB = {1, 3, 5, 7}Answer the questions below:•Find n(B).
•Find the set A B.
•Find the set .
•Find the set .
B
BA
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Given the sets U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},A = {0, 2, 4, 5, 6, 8}, andB = {1, 3, 5, 7}Answer the questions below:•Is 7A true or false?
•Is 5B true or false?
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Cardinal Number Formula for the Union of Sets
n(AB) = n(A) + n(B) — n(AB)
Formulas
Cardinal Number Formula for the Complement of a Set
n(U) = n(A) + n(A )
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If n(AB) = 40, find n(AB) and draw a Venn diagram to illustrate the composition of U.
Suppose n(U) = 61, n(A) = 32, and n(B) = 26.
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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)
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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.
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Cards
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Cards
Determine how many cards, in an ordinary deck of 52, are clubs or twos.
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Cards
Determine how many cards, in an ordinary deck of 52, are face cards or diamonds.
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Cards
Determine how many cards, in an ordinary deck of 52, are threes or sixes.
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Cards
Determine how many cards, in an ordinary deck of 52, are threes and sixes.