1. Write
the following set in the builder notation form {7,12,17,22,27,32,37,42,47,52}
2. List
the elements of the given set in roster notation {x|7 –x=9; x, an integer}
3. List
all subsets of the sets {8, 1, 3}
4. Find
the smallest possible set (that is, the set with the least numbers of elements)
that contains the given set as subsets. {6, 1, 3}, {a,e}
5. Find
the smallest possible set (that is, the set with the least numbers of elements)
that contains the given set as subsets. {Volkswagen, GM, Nissan}, {Porche,
Volvo, Chrysler}
6. Use
Venn diagrams to illustrate the statement A u A u B (the first u supposed to be
turn side ways).
7. Shade
the portion of the accompanying figure that represents the sets (A u B)^c n C
8. Determine
whether the given pair of sets is disjoint. {2,3,4,5} {4,5,6,7}
9. Let A=
{2,4,6,8} and B= {2,3,5,7,9} Compute n (A).
10. In a survey of 122 consumers conducted in a
shopping mall, 82 consumers indicated that they buy brand A of a certain
product, 71 buy brand B, and 46 buy both brands. How many consumers
participating in the survey buy only brand A?
11. In a poll conducted among 180 active investors, it was found that
100 use discount brokers, 122 use full-service brokers, and 54 use both
discount and full-service brokers. How many investors use only discount brokers?
12. On a certain day, the Wilton County Jail had 183 prisoners.
Of these, 127 were accused of felonies, and 117 were accused of misdemeanors.
How many prisoners were accused of both a felony and a misdemeanor?
13. If n (A)=12, n (A n B)=8, and n(A uB)=18,
what is n(B)?
14. Let A and B be subsets of a universal set U
and suppose ^n(U)=210, n(A)=100, n(B)=60 and n(A n B)=30. Compute ^n (A^c n
B^c).
15. Let A and B be subsets of a universal set U
and suppose ^n(U)=190, n(A)=100, n(B)=70 and n(A n B)=50. Compute ^n (A^c).
16. A survey of 900 subscribers to the Los
Angeles Times revealed that 700 people subscribe to the daily morning edition
and 400 subscribe to both the daily and the Sunday editions.How many subscribe
to the Sunday edition?
17. Three different types of monthly commuter
passes are offered by a city’s local transit authority for three different
groups of passengers. How many different kinds of passes must be possible?
18. In a card game, a 2-card hand consisting of
an ace and either a face card of diamond or a 10 is called a “win”. If a
standard 52-card deck is used, determine how many winning hands can be dealt.(A
“face card” is a jack, queen, or king.)
19. An opinion poll is to be conducted among
cable TV viewers. Four multiple-choice questions, each with three possible
answers, will be asked. In how many different ways can a viewer complete the
poll if exactly one response is given to each question?
20. A warranty identification number for a certain
product consists of a letter of the alphabet followed by a four-digit number.
How many possible identification numbers are there if the first digit of the
four-digit number must be nonzero?
21. An exam consists of six true-or-false
questions. Assuming that every question is answered, in how many different ways
can a student complete the exam? In how many ways may the exam be completed if
a penalty is imposed for each incorrect answer, so that a student may leave
some questions unanswered?
22. A Social Security number has seven digits.
How many Social Security numbers are possible?
23. In a survey conducted by a union, members
were asked to rate the importance of the following issues: (1) job security,
(2) increased fringe benefits, and (3) improved working conditions. Six
different responses were allowed for each issue. Among completed surveys, how
many different responses to this survey were possible?
24. The 2010 BMW 335i Coupe is offered with a
choice of 9 exterior colors (7 metallic and 2 standard), 5 interior colors, and
4 trims. How many combinations involving color and trim are available for the
model?
25. How many international direct-dialing
numbers are possible if each number consists of a four-digit area code (the
first digit of which must be nonzero) and an eight-digit telephone number (the
first digit must be nonzero)?
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