Deck 6: Sets and Counting

Question 1

Let . ​ ​

A) false
B) true

Answer 1

false

Question 2

Find the smallest possible set (that is, the set with the least number of elements) that contains the given sets as subsets. ​ ​

A)
B)
C)
D)

Answer 2

Question 3

Let and . Find the set . ​

A)
B)
C)
D)

Answer 3

Question 4

Let U denotes the set of all students who applied for admission to fresman class at faber college for the upcoming academic year, and let Determine which of the following statements are true. i) ii) iii)

A) ii) only
B) ii) and iii) only
C) i) only
D) i) and ii) only
E) All are true

Question 5

Use venn daigram to illustrate the statement. ​

A) ​
B)
C) ​
D)
E) ​

Question 6

Write the following set in builder notation form. The set gold medalists in the Winter Olympic Games.
​

A) {x = x is a gold medalist in the Winter Olympic Games}
B) {x is a gold medalist in the Olympic Games}
C) {x | x is a gold medalist in the Winter Olympic Games}
D) {x is a gold medalist in the Winter Olympic Games}
E) {x is a player in the Olympic Games}

Question 7

​

Question 8

Determine whether the given pair of sets is disjoint. ​ ​

A) Not disjoint
B) Disjoint

Question 9

Find the smallest possible set (that is, the set with the least number of elements) that contains the given sets as subsets. ​ ​

A)
B)
C)
D)

Question 10

List the elements of the given set in roster notation. ​ ​

A)
B)
C)
D)

Question 11

Let U denote the set of all employees at Universal Life Insurance Company. Let ​ ​
Describe the set in words.
​

A) All employees who drink tea and coffee
B) All employees who drink tea but do not drink coffee
C) All employees who drink coffee but do not drink tea
D) All employees who drink tea or coffee

Question 12

Shade the portion of the accompanying figure that represents the set. ​ ​

A)
B)
C)
D)
E)

Question 13

Let U denote the set of all employees in a hospital. Let ​ ​
Describe the set in words.
​ ​

A) The set of all employees in a hospital who are male doctors.
B) The set of all employees in a hospital who are male administrators.
C) The set of all employees in a hospital who are female doctors.
D) The set of all employees in a hospital who are female administrators.
E) The set of all employees in a hospital who are both doctors and administrators.

Question 14

Write the following set in builder notation form ​

A)
B)
C)
D)
E)

Question 15

Use Venn diagrams to illustrate the statement. ​ ​

A)
B)
C)
D)
E)

Question 16

​

Question 17

Let U denotes the set of all students who applied for admission to fresman class at faber college for the upcoming academic year, and let Select the correct choice of venn daigram to describe the above sets.

A)
B)
C)
D)
E)

Question 18

List the elements of the given set in roster notation. ​ ​

A)
B)
C)
D)

Question 19

Let U denote the set of all senators in Congress. Let ​ ​
Write the set that represents the following statement:
​
The set of all Republicans who are female and are lawyers.
​

A)
B)
C)
D)

Question 20

List all subsets of the set . ​

A)
B)
C)
D)

Question 21

Let U denote the set of all senators in Congress. Let
​ ​
Write the set that represents the following statement:
​
The set of all Democrats who are lawyers.

Question 22

Refer to the accompanying figure and find the points that belong the set .
​

Question 23

Let . Which of the following sets are equal to A? ​

A)
B)
C)
D)

Question 24

Refer to the accompanying figure and find the points that belong the set .

Question 25

Refer to the accompanying figure and find the points that belong the set . ​ ​

A) t, s, x
B) t, s, x, r
C) t, s, y
D) y, r

Question 26

Refer to the following diagram where U is the set of all tourists surveyed over a 1-week period in London and ​ ​
​ ​
Express regions 2, 5, 6, and 8 together in set notation and in words.
​

A) ; The set of tourists who have not taken the underground over a 1-wk period in London
B) ; The set of tourists who have not taken a bus over a 1-wk period in London
C) ; The set of tourists who have not taken the underground over a 1-wk period in London.
D) ; The set of tourists who have not taken a cab over a 1-wk period in London
E) ; The set of tourists who have not taken a cab over a 1-wk period in London.

Question 27

Find the smallest possible set (that is, the set with the least number of elements) that contains the given sets as subsets.
​

Question 28

Let . Which of the following sets are equal to A?
​

Question 29

Let U denote the set of all senators in Congress. Let
​ ​
Write the set that represents the following statement:
​
The set of all Democrats who are female and are lawyers.

Question 30

Refer to the accompanying figure and find the points that belong to the set. ​ ​ ​

A) r
B) s, t
C) x, y
D) v
E)

Question 31

Refer to the accompanying figure and find the points that belong the set .
​

Question 32

List the elements of the given set in roster notation.
​

Question 33

Let ​ ​
Verify by direct computation the equation.
​ ​

A) Since and we verified that
​
B) Since and we verified that
​
C) Since and we verified that
​
D) Since and we verified that
​
E) Since and we verified that
​

Question 34

List all subsets of the set .

Question 35

Let and . Find the set .

Question 36

Let U denote the set of all senators in Congress. Let ​ ​
Write the set that represents the following statement:
​
The set of all Democrats who are lawyers.
​

A)
B)
C)
D)

Question 37

Refer to the accompanying figure and find the points that belong the set . ​ ​

A) x, z, w, r, v, u
B) s, x
C) x, z, w, r, v, u, s
D) u, s

Question 38

List the elements of the given set in roster notation.
​

Question 39

Refer to the accompanying figure and find the points that belong to the set .

A) u
B) w
C) w, r
D)

Question 40

Find the smallest possible set (that is, the set with the least number of elements) that contains the given sets as subsets.
​

Question 41

In a survey of 122 consumers conducted in a shopping mall, 83 consumers indicated that they buy brand A of a certain product, 69 buy brand B, and 46 buy both brands. How many consumers participating in the survey buy at least one of these brands? ​

A) 20 consumers
B) 28 consumers
C) 18 consumers
D) 106 consumers
E) 48 consumers
F) 30 consumers

Question 42

State whether the given statement is true or false.
​

Question 43

Refer to the accompanying figure and find the points that belong to the set.

Question 44

Let A, B, and C be subsets of a universal set U and suppose , , , , , , , and . ​
Compute .
​

A) 38
B) 33
C) 19
D) 24
E) 34
F) 9

Question 45

State whether the given statement is true or false.

Question 46

Shade the portion of the accompanying figure that represents each set.
Match each figure below with the letter of the corresponding set.
a. b.

Question 47

Results of a Department of Education survey of SAT test scores in showed that states had an average composite SAT score of at least 1000 during the past 3 years. 17 states had an increase of at least 10 points in the average composite SAT score during the past 3 years.
9 states had both an average composite SAT score of at least 1000 and an increase in the average composite SAT score of at least 10 points during the past 3 years.
​
How many of these states had composite scores less than 1000 and showed an increase of
At least 10 points over 3-year period?

A)
B)
​
C)
D)
E)

Question 48

Let A, B, and C be subsets of a universal set U and suppose , , , , , , , and . ​
Compute .
​

A) 39
B) 14
C) 10
D) 70
E) 89
F) 64

Question 49

Let . Determine whether the given statement is true or false.
​

Question 50

Let U denote the set of all employees at Universal Life Insurance Company. Let
​ ​
Match each description below with the letter of the corresponding set.
​
a. b. c. d.
drinks tea and coffee

Question 51

In a survey of 250 households regarding the ownership of desktop and laptop computers, the following information was obtained: ​
130 households own only desktop computers.
​ 30 households own only laptop computers.
​ 50 households own neither desktop nor laptop computers.
​
How many households own both desktop and laptop computers?
​

A) 40 households
B) 80 households
C) 100 households
D) 10 households
E) 90 households
F) 81 prisoners

Question 52

Let U denote the set of all employees at Universal Life Insurance Company. Let
​ ​
Match each description below with the letter of the corresponding set.
​
a. b. c. d.
drinks tea but does not drink coffee

Question 53

Let U denote the set of all employees at Universal Life Insurance Company. Let
​ ​
Match each description below with the letter of the corresponding set.
​
a. b. c. d.
drinks coffee but does not drink tea

Question 54

Shade the portion of the accompanying figure that represents each set.
Match each figure below with the letter of the corresponding set.
a. b.

Question 55

In a survey of 380 households regarding the ownership of VCRs and DVD players, the following data was obtained: ​
350 households own one or more VCRs.
​
180 households own one or more VCRs and one or more DVD players.
​ 13 households do not own a VCR or a DVD player.
​
How many households only own one or more DVD players?
​

A) 30 households
B) 19 households
C) 16 households
D) 29 households
E) 20 households
F) 50 households

Question 56

Let Verify by direct computation each equation.
a.
b.

Question 57

Determine whether the given pair of sets is disjoint. Answer yes or no.
​

Question 58

Let and . Compute n(A). ​

A) 4
B) 14
C) 8
D) 17
E) 5
F) 1

Question 59

Let U denote the set of all employees in a hospital.
Let Describe each set in words.
a.
b.

Question 60

Let U denote the set of all employees at Universal Life Insurance Company. Let
​ ​
Match each description below with the letter of the corresponding set.
​
a. b. c. d.
drinks tea or coffee

Question 61

If , , , , , , and , find . ​

A) 18
B) 15
C) 20
D) 11
E) 10
F) 14

Question 62

Let A and B be subsets of a universal set U and suppose , , , and . Compute . ​

A) 40
B) 90
C) 30
D) 20
E) 170
F) 10

Question 63

A survey of 100 college students who frequent the reading lounge of a university revealed the following results:
​
47 read Time.
​
36 read Newsweek.
​
31 read U.S. News & World Report.
​
19 read Time and Newsweek.
​
16 read Time and U.S. News & World Report.
​
12 read Newsweek and U.S. News & World Report.
​
6 read all three magazines.
​
How many of the students surveyed read none of these magazines?
​
__________ students

Question 64

In a poll conducted among active investors, it was found that use discount brokers, use full-service brokers, and use both discount and full-service brokers. How many investors use only discount brokers? ​

A)
B)
C)
D)
E)

Question 65

In a survey of 300 individual investors regarding subscriptions to the New York Times (NYT), Wall Street Journal (WSJ), and USA Today (UST), the following data were obtained: ​
122 subscribe to the NYT.
​
151 subscribe to the WSJ.
​
63 subscribe to the UST.
​
39 subscribe to the NYT and WSJ.
​
29 subscribe to the WSJ and UST.
​
18 subscribe to the NYT and UST.
​
35 do not subscribe to any of these newspapers.
​
How many subscribe to only one of these newspapers?
​

A) 244
B) 229
C) 179
D) 209
E) 194

Question 66

A survey of the opinions of leading Economists in a certain country showed that, because oil prices were expected to drop in that country over the next 12 months, had lowered their estimate of the consumer inflation rate, had raised their estimate of the gross national product (GNP) growth rate. had lowered their estimate of the consumer inflation rate but had not raised their estimate of the GNP growth rate. How many Economists had raised their estimate of GNP growth rate and lowered their estimate of the consumer inflation rate for that period?
​

A)
B)
C)
D)
E)

Question 67

Of 55 employees of a store located in downtown Boston, 16 people take the subway to work, 11 take the bus, and 6 take both the subway and the bus. How many employees take either the bus or the subway to work? ​

A) 34
B) 10
C) 21
D) 15
E) 5

Question 68

The 120 consumers were asked about their buying preferences concerning another product that is sold in the market under three labels. The results were ​
12 buy only those sold under label A.
​
24 buy only those sold under label B.
​
27 buy only those sold under label C.
​
14 buy only those sold under labels A and B.
​
9 buy only those sold under labels A and C.
​
11 buy only those sold under labels B and C.
​
7 buy the product sold under all three labels.
​
How many of the consumers surveyed buy the product sold under none of these labels?
​

A) 81
B) 16
C) 12
D) 32
E) 104

Question 69

Of 100 clock radios sold recently in a department store, 60 had FM circuitry, and 80 had AM circuitry. How many could receive FM transmission only? ​

A) 50
B) 10
C) 20
D) 60
E) 40

Question 70

If , , and , what is ? ​

A) 17
B) 8
C) 15
D) 13
E) 6
F) 14

Question 71

In a survey of 370 households regarding the ownership of VCRs and DVD players, the following data was obtained:
​
340 households own one or more VCRs.
​
170 households own one or more VCRs and one or more DVD players.
​
18 households do not own a VCR or a DVD player.
​
How many households only own one or more DVD players?
​
__________ households

Question 72

If , , and , what is ? ​

A) 1
B) 12
C) 5
D) 2
E) 3
F) 9

Question 73

Data released by the Department of Education regarding the rate (percentage) of ninth-grade students that don't graduate showed that out of 50 states, ​
16 states had an increase in the dropout rate during the past 2 years.
​
18 states had a dropout rate of at least 30% during the past 2 years.
​
20 states had an increase in the dropout rate and/or a dropout rate of at least 30% during the past 2 years.
​
How many states had a dropout rate that was less than 30% but that had increased over the 2-year period?
​

A) 14
B) 32
C) 30
D) 2
E) 4

Question 74

In a survey of 200 households regarding the ownership of desktop and laptop computers, the following information was obtained:
​
110 households own only desktop computers.
​
10 households own only laptop computers.
​
50 households own neither desktop nor laptop computers.
​
How many households own both desktop and laptop computers?
​
__________ households

Question 75

In a survey of members of a local sports club, members indicated that they plan to attend the next Summer Olympic Games, indicated that they plan to attend the next Winter Olympic Games, and indicated that they plan to attend both games. How many members of the club plan to attend at least one of the two game? ​

A)
B)
C)
D)
E)

Question 76

On a certain day, the Wilton County Jail had 184 prisoners. Of these, 128 were accused of felonies, and 117 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor? ​

A) 76 prisoners
B) 61 prisoners
C) 71 prisoners
D) 82 prisoners
E) 62 prisoners
F) 81 prisoners

Question 77

On a certain day, the Wilton County Jail had 190 prisoners. Of these, 129 were accused of felonies, and 122 were accused of misdemeanors. How many prisoners were accused of both a felony and a misdemeanor?
​
__________ prisoners

Question 78

If , , , , , , and find . ​

A)
B)
C)
D)
E)

Question 79

To help plan the number of meals to be prepared in a college cafeteria, a survey was conducted, and the following data were obtained:
​
133 students ate breakfast.
​
184 students ate lunch.
​
278 students ate dinner.
​
71 students ate breakfast and lunch.
​
113 students ate breakfast and dinner.
​
92 students ate lunch and dinner.
​
59 students ate all three meals.
​
How many of the students ate exactly one meal in the cafeteria?
​
__________ students

Question 80

Let A and B be subsets of a universal set U and suppose , , , and . Compute . ​

A) 80
B) 100
C) 90
D) 200
E) 150
F) 180