Deck 2: The Nature of Sets

Question 1

Show that the set is infinite by placing it into a one-to-one correspondence with a proper subset of itself.
​

Answer 1

We can show that the set can be placed into a one-to-one correspondence with a proper subset of itself :
​ ​
Since is a proper subset of A, we see that the set is infinite.

Question 2

Determine whether the statement is true or false.
If two sets are uncountable, then they are equivalent.

Answer 2

False

Question 3

Use set notation to identify the shaded region. ​ ​

A)
B)
C)
D)
E)

Answer 3

Question 4

Determine whether the statement is true or false.
​
All infinite sets are uncountable.

Question 5

Decide whether the set is countably infinite. ​
Set of whole numbers.
​

A) no
B) yes

Question 6

Show that the set is infinite by placing it into a one-to-one correspondence with a proper subset of itself. ​ ​

A) ​
​
B) ​
​
C) ​ ​
D) ​
​
E) ​
​

Question 7

Determine whether the statement is true or false.
​
All countable sets are infinite.
​

Question 8

Give the cardinality of the set ​ ​

A) 1,087
B) 1,089
C) 1,088
D) 1,084
E) 1,093

Question 9

Show that the set has cardinality . ​
Set of multiples of 5.
​

A) ​
B) ​
C)
D)
E) ​

Question 10

Show that the set has cardinality .
​
{- 1, - 2, - 3, ...}

Question 11

If and , what is ?

Question 12

If and , what is ? ​

A) ​2,600
B) 800
C) 80
D) 100
E) 250

Question 13

Decide whether the set is countably infinite. Answer yes or no.
​
Set of even numbers.

Question 14

Consider the sets X and Y. Write the statement in symbols. ​
The complement of the intersection of X and Y.
​

A)
B)
C)
D)
E)

Question 15

Show that the set has cardinality . ​

A)
B)
C)
D)
E)

Question 16

Show that the set has cardinality .
​
Set of even counting numbers.

Question 17

Give the cardinality of the set
​

Question 18

Determine whether the statement is true or false.
​
If two sets are equivalent, then they are countable.
​

Question 19

Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 6}, B = {1, 2, 6, 7}, C = {3, 6, 7}. List all the members of the set. ​ ​

A) {2, 4, 6}
B) {1, 2, 6, 7}
C) {1, 2, 3, 6}
D) {4, 5, 6, 7}
E) {6}

Question 20

Using the Venn diagram in the figure, specify which regions are described by each expression: ​ , ​ ​

A) Region 31, Region 5
B) Region 24, Region 2
C) Region 32, Region 3
D) Region 28, Region 4
E) Region 32, Region 31

Question 21

Perform the given set operation. ​
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}.
​ ​

A) {1, 3, 5 ,7}
B) {2, 4, 6}
C) {1, 2, 3, 4, 5, 6, 7, 8}
D) {2, 4, 6, 8, 10}
E) {1, 3, 5, 7, 9}

Question 22

Perform the given operations. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (U represents the universal set). ​ ​

A)
B)
C)
D)
E)

Question 23

Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 5}, B = {1, 2, 5, 6}, C = {3, 5, 7}. List all the members of the set below.
​ ​
{ __________ }

Question 24

Draw a Venn diagram for the relationship. ​ ​

A) ​
B) ​
C) ​
D) ​

Question 25

Use set notation to identify the shaded region.
​ ​
Please enter parentheses to indicate the order of operations.

Question 26

Draw a Venn diagram showing birds, bees, and living creatures. ​

A)
B)
C)
D)
E)

Question 27

Perform the given set operation. ​
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
​ ​

A) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B) {1, 3, 5, 7, 9}
C) {2, 4, 6, 8, 10}
D) {1, 2, 3, 4, 5, 6, 7}
E)

Question 28

A poll was taken of 214 students at a commuter campus to find out how they got to campus. How many used none of the mentioned means of transportation? The results of the poll were:
34 said they drove alone.
31 rode in a carpool.
35 rode public transportation.
8 used both carpools and public transportation.
7 used both a carpool and sometimes their own cars.
9 used buses as well as their own cars.
8 used all three methods.
​
__________ students

Question 29

Draw Venn diagrams for the relationship ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 30

Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 4} and C = {2, 5, 6}. List all the members of the following set. ​ ​

A) {1, 2, 3, 4, 5, 6}
B) {1, 3, 4, 7}
C) {1, 2, 3, 4}
D) {2, 5, 6}
E)

Question 31

In a survey of a TriDelta chapter with 50 members, 16 were taking mathematics, 34 were taking English, and 5 were taking both. How many were not taking either of these subjects?
​
__________ members

Question 32

In a survey of a TriDelta chapter with 46 members, 11 were taking mathematics, 36 were taking English, and 10 were taking both. How many were not taking either of these subjects? ​

A) 11
B) 6
C) 36
D) 9
E) 10

Question 33

Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 5} and C = {1, 4, 7}. List all the members of the following set. ​ ​

A)
B)
C)
D)
E)

Question 34

Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 5} and C = {3, 4, 6}. List all the members of the following set. ​ ​

A)
B)
C)
D)
E)

Question 35

Montgomery College has a 47-piece band and a 43-piece orchestra. If 18 people are members of both the band and the orchestra, can the band and orchestra travel in two 37-passenger buses? ​

A) yes
B) no

Question 36

Perform the given operation. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (U represents the universal set). ​ ​

A)
B)
C)
D)
E)

Question 37

Using the Venn diagram in the figure, specify which regions are described by each expression:
​ , ​ ​ describes the region number __________.
​ describes the region number __________.

Question 38

Draw Venn diagrams for the relationship ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 39

Consider the sets X and Y. Write the statement in symbols.
​
The complement of the union of X and Y.
​
Enter to represent .

Question 40

The fire department wants to send booklets on fire hazards to all teachers and homeowners in town. How many booklets does it need, using these statistics? 35,000 homeowners
6,000 teachers
3,000 teachers who own their own homes
​

A) 9,000
B) 32,000
C) 38,000
D) 26,000
E) 44,000

Question 41

Consider the set ​
A = {distinct letters in the word pipe}
​
What is the cardinality of it?
​

A) 9
B) 3
C) 10
D) 2
E) 5

Question 42

Perform the given operation. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (U represents the universal set).
​ ​
Enter your answer using set notation.

Question 43

List the set in roster form. ​ ​

A) 2, 3, 4, 5, 6, 7, 8, 9, 10
B) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
C) 2, 4, 6, 8, 10, 12, 14
D) 1, 3, 5, 7, 9, 11, 13
E) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15

Question 44

Montgomery College has a 50-piece band and a 36-piece orchestra. If 14 people are members of both the band and the orchestra, can the band and orchestra travel in two 40-passenger buses?
​
Answer yes or no.

Question 45

Tell whether the set is well defined. If it is not well defined, change it so that it is well defined.
​
The set of students attending the University of California.
​
__________ (well defined, not well defined)
​
a. The set of students attending the University of California.
b. The set of students attending the Massachusetts Institute of Technology.
c. The set of students attending the University of Berkeley.
d. The set of students attending Boston University.
e. None of these because the set is well defined.

Question 46

Perform the given operation. Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (U represents the universal set).
​ ​
Enter your answer using set notation.

Question 47

Specify the set by roster.
​
{Counting numbers containing only 4s.}
​
Enter the first four terms of the set.

Question 48

Consider the set
​
A = {distinct letters in the word tank}
​
What is the cardinality of it?

Question 49

Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 5} and C = {3, 4, 7}. List all the members of the set.
​ ​
Enter your answer using set notation.

Question 50

Tell whether the set is well defined. ​
{Good bets on the next race at Hialeah.}
​

A) well defined
B) not well defined

Question 51

Decide whether the statement is true or false. ​ ​

Question 52

"All sparrows are birds". Rephrase this using set terminology. ​

A) The set of sparrows is not a subset of the set of birds
B) Some birds are a subset of the set of sparrows, and some are not
C) The set of birds is a subset of the set of sparrows
D) Some sparrows are a subset of the set of birds, and some are not
E) The set of sparrows is a subset of the set of birds

Question 53

Consider the sets ​ ​ ​
Which of the sets are equivalent?
​

A)
B)
C)
D)
E) ​

Question 54

Perform the given set operation.
​
Let U = {1, 2, 3, 4, 5, 6, 7, 8}.
​ ​
Enter your answer in a set notation.

Question 55

Perform the given set operation.
​
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
​

Question 56

Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 5} and C = {1, 4, 7}. List all the members of the set.
​ ​
Enter your answer using set notation.

Question 57

Write out in words the description of the given set, and then list the set in roster form.
​ ​
This is a set of whole numbers where the terms are __________ than __________.
​
Enter the terms of the set.

Question 58

Let U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 3, 5} and C = {1, 4, 6}. List all the members of the set.
​ ​
Enter your answer using set notation.

Question 59

Decide whether the statement is true or false.
​ ​

Question 60

Specify the set by roster. ​
{Counting numbers containing only 4s.}
​

A) 41, 42, 43, 44, ...
B) 44, 444, 4444, 44444, ...
C) 4, 444, 44444, 4444444, ...
D) 4, 44, 444, 4444, ...
E) 4, 14, 24, 34, 44, ...

Question 61

Decide whether the statement is true or false.
​

Question 62

"All Boeings are airplanes". Rephrase this using set terminology.

Question 63

Consider the sets
​ ​
Which of the sets are equivalent?

Question 64

Decide whether the statement is true or false.
​ ​