# Work each problem and show all work please

**Question description**

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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