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Practice Exam 1

 

Name___________________________________

 

 

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

 

Determine whether the set is well defined.

1)

The set of the best luggage

 

1)

 

A) not well defined

B) well defined

 

2)

The set of five countries in Europe having the smallest population

2)

 

A) not well defined

B) well defined

 

Identify the set as finite or infinite.

3)

{8, 9, 10, . . ., 32}

 

 

3)

 

 

A) Infinite

 

B) Finite

 

 

4)

{1,

1

,

1

,

1

, . . .}

 

 

4)

 

 

16

64

 

 

 

 

4

 

 

 

 

 

 

 

 

A) Finite

 

B) Infinite

 

 

5)

{x|x is a fraction between 67 and 68}

 

5)

 

 

A) Infinite

 

B) Finite

 

 

Express the set in roster form.

 

 

 

 

6)

{x|x is a whole number between 3 and 7}

 

6)

 

 

A) {4, 5, 6, 7}

B) {3, 4, 5, 6}

C) {4, 5, 6}

D) {3, 4, 5, 6, 7}

 

7)

{x|x is an integer between 6 and 10}

 

7)

 

 

A) {7, 8, 9}

B) {6, 7, 8, 9}

C) {6, 7, 8, 9, 10}

D) {7, 8, 9, 10}

 

8)

The set of the days of the week

 

8)

 

A)  {Tuesday, Thursday}

B)  {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}

C)  {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday}

D)  {Saturday, Sunday}

Tell whether the statement is true or false. If false, give the reason.

9)

10   {20, 30, 40, 50, 60}

9)

 

A) True

B) False; 10 is a set.

 

C) False; 10 is a factor of the elements.

D) False; 10 is not an element of the set.

10)

{2, 10, 13} = {0, 2, 10, 13}

10)

 

A) False; 0 must be an element of both sets.

B) True

 

C) False; each set must have 4 elements.

D) False; 0 is not a valid member of a set.


 

 

 

 

 

 

 

 

1


11)  17   {16, 14, 13, . . ., 1}

 

A)  False; 17 is an element of the set.

B)  False; 17 is smaller than the elements of the set.

C)  True

D)  False; 17 is a set.

 

Find n(A) for the set.

12)

A = {200, 201, 202, . . ., 2000}

 

 

 

A) n(A) = 1801

B) n(A) = 4

C) n(A) = 1800

13)

A = {3, 5, 7, 9, 11}

 

 

 

A) n(A) = 5

B) n(A) = 2

C) n(A) = 11

 

Determine whether the sets are equal, equivalent, both, or neither.

14)

{L, M, N, O} and {l, m, n, o}

 

 

 

A) Both

B) Equivalent

C) Neither

15)

{13, 85, 16} and {85, 16, 13}

 

 

 

A) Equal

B) Both

C) Equivalent

 

Let A = {1, 3, 5, 7}

B = {5, 6, 7, 8}

C = {5, 8}

D = {2, 5, 8}

U = {1, 2, 3, 4, 5, 6, 7, 8}.

Determine whether the statement is true or false.

16)  C   D

A)  False; C is not a subset of D.

B)  False; D is a subset of C.

C)  False; the elements are the same in C and D.

D)  True

 

17)  D   B

A)  False; the elements are the same.

B)  True

C)  False; the elements are not the same.

D)  False; the sets must have the same number of elements.

 

18)  A  {7, 5, 3, 1}

 

A)  False; A has different elements than those listed.

B)  True

C)  False; the elements in A are in a different order.

D)  False; the elements in A are the same as those listed.

 

Use  ,  ,  , or both   and   to make a true statement.

19)

{4, 5, 6}

{3, 4, 5, 6}

 

 

 

 

A)

 

 

B)   and

C)

 

20)

 

{8, 16, 27, 31}

 

 

 

 

 

 

 

B)

C)

 

 

 

A)

 

 

 

 

                 

11)

 

 

 

 

 

 

12)

D) n(A) = 2000

13)

D) n(A) = 4

 

14)

D) Equal

15)

D) Neither

 

 

 

 

 

 

 

 

16)

 

 

 

 

 

17)

 

 

 

 

 

18)

 

 

 

 

 

 

19)

D)

 

20)

D)   and


 

2


21) {11, 12, 13}

{11, 12, 13}

 

 

21)

 

A)

 

 

B)

C)   and

D)

 

 

 

 

List all subsets or determine the number of subsets as requested.

22)

Determine the number of subsets of {8, 9, 10}

 

22)

 

A) 7

B) 6

C) 3

D) 8

23)

List all the subsets of {bear, dog, sheep}.

 

23)

         

A)  {bear, dog}, {bear, sheep}, {dog, sheep}, {bear}, {dog}, {sheep}

B)  {bear, dog, sheep}, {bear, dog}, {bear, sheep}, {dog, sheep}, {bear}, {dog}, {sheep}, { }

C)  {bear, dog}, {bear, sheep}, {dog, sheep}, {bear}, {dog}, {sheep}, { }

D)  {bear, dog, sheep}, {bear, dog}, {bear, sheep}, {dog, sheep}, {bear}, {dog}, {sheep}

If the statement is true for all sets C and D, write "true." If it is not true for all sets C and D, write "false." Assume that C

, U, and C   U.

 

24)

C

24)

 

A) True

B) False

25)

C   U

25)

 

A) True

B) False

26)

U

26)

 

A) True

B) False

For the given sets, construct a Venn diagram and place the elements in the proper region.

27)

Let U = {c, d, g, h, k, u, q}

27)

 

A = {d, h, g, q}

 

 

B = {c, d, h, u}

 

 

 

 

 

 

 

 

A)                                                                        B)

 

 

 

 

 

 

 

 

Let U = {all soda pops}, A = {all diet soda pops},

B = {all cola soda pops}, C = {all soda pops in cans},

and D = {all caffeine-free soda pops}. Describe the

set in words.

28) A   B                                                                                                                                             28)

A) All diet cola soda pops                                      B) All diet or all cola soda pops

C) All diet and all cola soda pops                          D) All soda pops


 

 

3


29) A   B   D                                                                                                                                        29)

A) All soda pops not in cans                                  B) All diet and all cola and all caffeine-free

soda pops

C) All diet, caffeine-free cola soda pops                  D) All diet, caffeine-free cola pops in cans

 

 

Use the Venn diagram to list the set of elements in roster form.

30) Find A.

30)

9

x   p

 

6

3

h

 

A) {9, 3, 6}

 

B) {6, x, p, h}

C) {6}

D) {9, 3, 6, x}

 

31) Find A   B.

 

 

 

31)

 

h

e

b

 

 

 

n

j

u

 

 

 

m

 

 

 

 

 

A) {m}

 

 

B) {e, j}

 

 

C) {b, e, j, h, m, n, u}

D) {b, e, j, h, n, u}

 

 

32) Find (A   B)'.

 

 

 

32)

 

7

4

z   q

 

 

 

2

h

 

 

 

 

 

 

 

A) {7}

 

B) {7, 2, 4, z, q, h}

C)

D) {7, 2, 4}

 

Let U = {q, r, s, t, u, v, w, x, y, z}

A = {q, s, u, w, y}

B = {q, s, y, z}

C = {v, w, x, y, z}.

Determine the following.

33)

(A   B)'

 

 

33)

 

A) {r, s, t, u, v, w, x, z}

 

B) {s, u, w}

 

 

C) {t, v, x}

 

D) {r, t, v, x}

 

34)

A  (B   C)

 

 

34)

 

A) {q, y, z}

B) {q, s, u, w, y, z}

C) {q, r, w, y, z}

D) {q, w, y}


 

 

 

 

4


Let U = {q, r, s, t, u, v, w, x, y, z}

 

 

 

A = {q, s, u, w, y}

 

 

 

B = {q, s, y, z}

 

 

 

C = {v, w, x, y, z}

 

 

 

Determine the following.

 

 

 

35)

A   (B   C)

 

 

35)

 

A) {q, s, w, y}

B) {q, s, u, w, y, z}

C) {q, r, w, y, z}

D) {q, y, z}

36)

(A'   C)   B'

 

 

36)

 

A) {r, t, u, v, w, s, y, z}

 

B) {y, z}

 

 

C) {v, x}

 

D) {r, t, v, w, x}

 

Construct a Venn diagram illustrating the following sets.

 

 

37)

U = {2, 4, 6, 8, 10, 12}

 

 

37)

 

A = {2, 6, 10}

 

 

 

B = {2, 4, 8}

C = {2, 8, 10, 12}

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A)                                                                        B)


 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5


C)                                                                       D)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Use the Venn diagram shown to list the set in roster form.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

38)

B

38)

 

A) {4, 12}

B) {7, 14}

 

C) {4, 7, 11, 12, 14}

D) {0, 4, 7, 11, 12, 14}

39)

B  C

39)

 

A) {2, 4, 7, 8, 10, 11, 12, 13, 14}

B) {4, 11, 12}

 

C) {2, 4, 7, 8, 10, 12, 13, 14}

D) {2, 7, 8, 10,14}

40)

(A   B)'

40)

 

A) {1, 2, 3, 5, 6, 9, 10}

B) {11}

 

C) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14}

D) {1, 2, 5, 8, 10}

Use Venn diagrams to determine whether the following statements are equal for all sets A and B.

41) (A   B)', A'   B'

41)

A) equal

B) not equal

42) (A'   B)', A   B'

42)

A) equal

B) not equal


 

 

 

 

 

 

 

 

6


Solve the problem.

43)

Results of a survey of fifty students indicate that 30 like red jelly beans, 29 like green jelly beans,

43)

 

and 17 like both red and green jelly beans. How many of the students surveyed like red or green

 

 

jelly beans?

 

 

 

 

 

A) 13

B) 25

C) 17

D) 42

 

44)

Monticello residents were surveyed concerning their preferences for candidates Moore and Allen in

44)

 

an upcoming election. Of the 800 respondents, 300 support neither Moore nor Allen, 100 support

 

 

both Moore and Allen, and 250 support only Moore. How many residents support Allen?

 

 

A) 250

B) 400

C) 150

D) 100

 

45)

A local television station sends out questionnaires to determine if viewers would rather see a

45)

 

documentary, an interview show, or reruns of a game show. There were 300 responses with the

 

 

following results:

 

 

 

 

90 were interested in an interview show and a documentary, but not reruns. 12 were interested in an interview show and reruns but not a documentary 42 were interested in reruns but not an interview show.

 

72 were interested in an interview show but not a documentary. 30 were interested in a documentary and reruns.

18 were interested in an interview show and reruns.

24 were interested in none of the three.

 

How many are interested in exactly one kind of show?

A) 154

B) 144

C) 134

D) 124

46) A survey of 160 families showed that

 

46)

59 had a dog;

 

 

 

46 had a cat;

 

 

 

19 had a dog and a cat;

 

 

 

63 had neither a cat nor a dog nor a parakeet;

 

 

3 had a cat and dog and a parakeet.

 

 

How many had a parakeet only?

 

 

A) 21

B) 26

C) 16

D) 11

 


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