# Question 5 Let U represent the set of people in a certain community who were asked if they subscribe to an information source.

Question 5

Let  U  represent the set of people in a certain community who were asked if they subscribe to an information source.

Let D ={ x ∈ U  | x subscribes to

The Daily Informer

}

and

N ={ x ∈ U  | x subscribes to

News Magazine

}

(Assume these sets are not disjoint.)

Write the set that represents the set of people surveyed who subscribe to The Daily Informer but not News Magazine.

a)

D

b)

( N ∪ D )c

c)

N c ∪ D

d)

N c ∪ D c

e)

N c ∩ D

f)

None of the above.

Review Later

Question 6

Let  U  represent the set of all people that frequently visit a certain restaurant, surveyed about which food they like best. Let

B = { x ∈ U  |  x  likes Hamburgers }

C = { x ∈ U  |  x  likes Corn Dogs }

P = { x ∈ U  |  x  likes Pizza }

(Assume these sets are not disjoint.)

Write the statement that refers to: P ∩ ( C ∪ B ) c .

a)

The set of customers who like Pizza or Corn Dogs or Burgers.

b)

The set of customers who like all three foods given.

c)

The set of customers who like Pizza but not Corn Dogs or Burgers.

d)

The set of customers who like Pizza and Corn Dogs but not Burgers.

e)

The set of customers who do not like any of these foods given.

f)

None of the above.

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Question 7

Suppose that  S  is the set of successful students in a classroom, and that  F  stands for the set of freshmen students in that classroom. Find n(S∩ F) given that

n(S) = 60, n(F) = 22 and n(S ∪ F) = 63

a)

0

b)

145

c)

82

d)

19

e)

123

f)

None of the above.

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Question 8

Suppose that n(U) = 200, n(A) = 135, n(B) = 105, and n( A ∩ B ) = 50. Find n( A c ∪ B ).

a)

85

b)

65

c)

105

d)

115

e)

55

f)

None of the above.

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Question 9

A survey of 398 children given at a local elementary school showed that 175 like chocolate ice cream, 150 like pistachio ice cream, and 123 do not like chocolate or pistachio ice cream. How many children like both chocolate ice cream and pistachio ice cream?

a)

50

b)

275

c)

225

d)

125

e)

325

f)

None of the above.

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Question 10

412 students were surveyed about their preferences of sports. 145 students like football, 138 students like baseball, and 46 students like both sports. How many students do not like football or baseball?

a)

329

b)

138

c)

83

d)

175

e)

92

f)

None of the above.

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Question 11

428 students were surveyed about their preferences of sports. 146 students like football, 144 students like baseball, and 45 students like both sports. How many students like exactly one of the two sports?

a)

146

b)

290

c)

200

d)

99

e)

101

f)

None of the above.

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Question 12

A campus radio station surveyed 500 students to determine the types of music they like. The survey revealed that 198 like rock,163 like country, and 120 like jazz. Moreover, 23 like rock and country, 20 like rock and jazz, 25 like country and jazz, and 5 like all three types of music. How many students surveyed liked rock only? (Note: A Venn diagram may be useful here.)

a)

155

b)

140

c)

198

d)

160

e)

142

f)

None of the above.

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Question 13

A survey of 500 high school students was taken to determine their favorite chocolate candy. Of the 500 students surveyed, 129 like Snickers, 118 like Twix, 145 like Reese’s Peanut Butter Cups, 22 like Snickers and Twix, 54 like Twix and Reese’s Peanut Butter Cups, 55 like Snickers and Reese’s Peanut Butter Cups, and 8 like all three kinds of chocolate candy. How many students like at most 2 kinds of these chocolate candies?

a)

107

b)

60

c)

261

d)

492

e)

115

f)

None of the above.

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Question 14

A survey of 500 high school students was taken to determine their favorite chocolate candy. Of the 500 students surveyed, 143 like Snickers, 130 like Twix, 163 like Reese’s Peanut Butter Cups, 51 like Snickers and Twix, 43 like Twix and Reese’s Peanut Butter Cups, 86 like Snickers and Reese’s Peanut Butter Cups, and 34 like all three kinds of chocolate candy. How many students like Reese’s Peanut Butter Cups or Snickers, but not Twix?

a)

186

b)

92

c)

160

d)

108

e)

194

f)

None of the above.

Review Later

Question 15

(Car Sales)

Of the cars sold during the month of July, 87 had air conditioning, 99 had automatic transmission, and 73 had power steering. 8 cars had all three of these extras. 24 cars had none of these extras. 24 cars had only air conditioning, 64 cars had only automatic transmissions, and 35 cars had only power steering. 9 cars had both automatic transmission and power steering. How many cars had exactly two of the given options?

a)

64

b)

56

c)

96

d)

1

e)

82

f)

None of the above.