Deck 2: Sets

Question 1

Write the set using set-builder notation:
The set of natural numbers greater than 11.

A){12, 13, 14, 15, . . .}
B)
C){11, 12, 13, 14, . . .}
D)

Answer 1

B

Question 2

Write the set using the descriptive method:
{25, 26, 27, . . . , 45}

Answer 2

The set of natural numbers from 25 to 45, inclusive.

Question 3

Show that the pair of sets is equivalent by using a one-to-one correspondence.
{ is an odd natural number between 8 and 20} and
{x is an even natural number between 13 and 25}

A)
B)
C)
D)

Answer 3

B

Question 4

List the elements in the set: {7, 10, 13, . . . , 31}.

Question 5

Write the set using roster notation:
The set of even natural numbers less than 10.

A)
B)
C){2, 4, 6, 8, 10}
D){2, 4, 6, 8}

Question 6

Let U = {5, 10, 15, 20, 25, 30, 35, 40}
A = {5, 10, 15, 20}
B = {25, 30, 35, 40}
C = {10, 20, 30, 40}.
Find C'.

A)C' = {5, 15, 25, 35}
B)C' = {5, 10, 15, 20, 25, 30, 35, 40}
C)C' = {10, 20, 30, 40}
D)

Question 7

Which statement is true?

A) }
B)
C)
D)All equivalent sets are equal.

Question 8

Let U = {8, 16, 24, 32, 40, 48, 56, 64} and A = {24, 32, 40, 56}.

A)
B)
C)
D)

Question 9

State whether the following set is empty.

A)Yes
B)No

Question 10

Which set is infinite?

A)
B)
C)
D){3, 5, 7, . . ., 99}

Question 11

Write the set using roster notation:

A){25, 26, 27, 28, . . .}
B)
C)
D){24, 25, 26, 27, . . .}

Question 12

Which set is finite?

A)
B){2, 4, 6, 8, 10, 12, . . .}
C)
D)

Question 13

Write the set using the descriptive method:
{9, 18, 27, 36, 45}

A)
B)The set natural numbers between 9 and 45.
C)
D)The set of the first five positive multiples of 9.

Question 14

Classify each pair of sets as equal, equivalent, or neither.
{1, 2, 3, . . ., 10} and {10, 9, 8, . . ., 1}

A)equal and equivalent
B)neither
C)equivalent

Question 15

State whether the collection is well-defined or not well-defined.
{5, . . . }

A)Well-defined
B)Not well-defined

Question 16

Find all subsets of the set. {2, 4, 9}.

Question 17

The graph below displays the median housing prices for all houses sold in Anywhere, US between 2003 and
2008. List the set of years in which the median price was above $150,000.

A)(2005, 2006, 2007, 2008}
B)(2003, 2004}
C)(2005, 2006, 2007}
D)(2003, 2004, 2008}

Question 18

Write the set using set-builder notation:
{1, 3, 5, . . . , 27}

A)
B)
C)
D)

Question 19

Classify each pair of sets as equal, equivalent, or neither.
{1, 3, 5} and {2, 4, 6, 8}

A)neither
B)equivalent
C)equal and equivalent

Question 20

Classify each pair of sets as equal, equivalent, or neither.
{a, b, c, d, e} and {5, 4, 3, 2, 1}

A)equivalent
B)neither
C)equal and equivalent

Question 21

Let U = {5, 10, 15, 20, 25, 30, 35, 40} = {5, 10, 15, 20} = {25, 30, 35, 40} = {10, 20, 30, 40}.
Find .

A) = {5, 10, 15, 20, 30, 40}
B)
C) = {10, 20}
D) = {5, 15, 30, 40}

Question 22

Draw a Venn diagram and shade the sections representing .

A)
B)
C)
D)

Question 23

Let U = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
X = {4, 6, 8, 10, 12, 14}
Y = {4, 5, 6, 7, 8, 9}
Z = {5, 7, 8, 9, 12, 13, 14}.

A)
B) = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
C) = {4, 5, 6, 7, 8, 9, 10, 12, 13, 14}
D)

Question 24

Find the number of proper subsets the set has. {m, n, p}

A)8
B)3
C)7
D)6

Question 25

True or False? {4} {2, 4, 6, 8, 10}

Question 26

Find all proper subsets of the set. {c, f, x}

A)
B)
C)
D)

Question 27

Find the number of subsets the set has. {1, 2, 3, 4, 5}

A)16
B)31
C)5
D)32

Question 28

Let = {n, p, q, r, s, t, u, v} = {n, p, q, r} = {n, q, s, u}.
Find B .

A) = {s, u}
B)
C) = {n, p, q, r, s, u}
D) = {s, t, u, v}

Question 29

Since the student union is being remodeled, there is a limited choice of foods and drinks a student
Can buy for a snack between classes. Students can choose none, some, or all of these items:
Diet soft drink, cheeseburger, fries. How many different selections can be made?

A)9
B)3
C)7
D)8

Question 30

Let = {5, 10, 15, 20, 25, 30, 35, 40} = {5, 10, 15, 20} = {25, 30, 35, 40} = {10, 20, 30, 40}.
Find ).

A) = 5, 10, 15, 20, 25, 30, 35, 40}
B)
C) = {10, 20, 25, 30, 35, 40}
D) )= {25, 35}

Question 31

Let = {5, 10, 15, 20, 25, 30, 35, 40} = {5, 10, 15, 20} = {25, 30, 35, 40} = {10, 20, 30, 40}.
Find A C.

A) = {5, 15, 30, 40}
B)
C) = {10, 20}
D) = {5, 10, 15, 20, 30, 40}

Question 32

Use the Venn diagram and find .

A) = {q, r, s, v, w}
B) = {q, r, s, v, w, x, y}
C) = {q, r, s, t, u, v, w}
D) = {t, u}

Question 33

Let U = {5, 10, 15, 20, 25, 30, 35, 40} = {5, 10, 15, 20} = {25, 30, 35, 40} = {10, 20, 30, 40}.

A) = {5, 15}
B) = {30, 40}
C)
D) = {25, 35}

Question 34

Draw a Venn diagram and shade the sections representing .

A)
B)
C)
D)

Question 35

Let = {5, 10, 15, 20, 25, 30, 35, 40} = {5, 10, 15, 20} = {25, 30, 35, 40} = {10, 20, 30, 40}.

A)
B) = {25, 35}
C) = {5, 10, 15, 20, 25, 30, 35, 40}
D) = {5, 15, 25, 30, 35, 40}

Question 36

Let U = {5, 10, 15, 20, 25, 30, 35, 40}
A = {5, 10, 15, 20}
B = {25, 30, 35, 40}
C = {10, 20, 30, 40}.

A)
B)
C)
D)

Question 37

True or False? {4} {2, 4, 6, 8, 10, . . . }

Question 38

Draw a Venn diagram and shade the sections representing .

A)
B)
C)
D)

Question 39

Which statement is false?

A)
B)
C)
D)

Question 40

Let = {1, 2, 3, . . . } = {4, 8, 12, 16, . . . } = {12, 24, 36, 48, . . . }.

A)
B)
C)
D)

Question 41

If = {Bob, Ann, Mae, Eve, Dan, Kim, Tal, Vic}, = {Ann, Eve, Dan, Kim}, and = {Bob, Ann, Mae, Eve} find

A)Both are {Ann, Eve}
B)
C)Both are {Tal, Vic}
D)Both are {Bob, Ann, Mae, Eve, Dan, Kim}

Question 42

{students running cross country}, {students swimming}, and {students running track}.
Draw a Venn diagram of , and write a sentence describing what the set represents.

A)
B)
C)
D)

Question 43

If = {Bob, Ann, Mae, Eve, Dan, Pat, Tal, Liz}, = {Ann, Eve, Dan, Pat}, and
B = {Bob, Ann, Mae, Eve} find

A)Both are {Bob, Mae, Eve, Dan, Pat}
B)
C)Both are {Ann, Eve}
D)Both are {Tal, Liz}

Question 44

Determine whether the two sets are equal.

Question 45

Determine whether the two sets are equal.

Question 46

Let U = { is a natural number 15} = { is an odd natural number} = { is a prime number}.
Find n( . Note: prime numbers are 2, 3, 5, 7 ,11, 13, 17, 19.

A)
B)
C)
D)

Question 47

Draw a Venn diagram and shade the sections representing

Question 48

In a survey of 29 instructors, it was found that 22 liked whiteboards, 11 liked blackboards, and 7
Liked both. How many instructors did not like whiteboards?

A)14
B)7
C)3
D)4

Question 49

The table shows the students from Genius High School with the four highest GPAs from 2005 to
2007. Write the region(s)of the Venn diagram that would include Harry. (Note set represents
2005 top-ranked students, set represents 2006 top-ranked students, and set represents 2007
Top-ranked students.)

A)Region II
B)Region VI
C)Region IV
D)Region V

Question 50

One weekend, there were 61 pizzas ordered for the sophomore dorm. That weekend 12 customers
Ordered their pizza with just pepperoni, 18 customers ordered their pizza with just sausage, 13
Ordered theirs with just onions, 6 ordered theirs with pepperoni and sausage, 5 ordered theirs with
Sausage and onions, 4 ordered theirs with pepperoni and onions, and 2 ordered theirs with all three
Items. The remaining pizzas were cheese pizzas with no toppings. How many customers ordered at
Most two toppings on their pizza?

A)58
B)15
C)16
D)59

Question 51

Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27
Contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12
Contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained
All three items. How many backpacks contained none of the three writing instruments?

A)2
B)15
C)11
D)3

Question 52

Draw a Venn diagram and shade the sections representing

A)
B)
C)
D)

Question 53

Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27
Contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12
Contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained
All three items. How many backpacks contained exactly one of the three writing instruments?

A)3
B)11
C)2
D)15

Question 54

Use the Venn diagram and find .

A)
B)
C)
D)

Question 55

In a group of 53 children, 22 had a dog, 18 had a cat, and 6 had both a dog and a cat. How many
Children had neither a dog nor a cat as a pet?

A)31
B)37
C)12
D)19

Question 56

Draw a Venn diagram and shade the sections representing

A)
B)
C)
D)

Question 57

Determine whether the two sets are equal.

A)not equal
B)equal

Question 58

One weekend, there were 98 pizzas ordered for the sophomore dorm. That weekend 19 customers
Ordered their pizza with just pepperoni, 16 customers ordered their pizza with just sausage, 20
Ordered theirs with just onions, 15 ordered theirs with pepperoni and sausage, 9 ordered theirs with
Sausage and onions, 17 ordered theirs with pepperoni and onions, and 2 ordered theirs with all three
Items. How many customers ordered their pizza with pepperoni or sausage (or both)?

A)72
B)35
C)50
D)13

Question 59

A = {people who drive a compact car} and {people who drive a diesel vehicle}. Draw a Venn
Diagram of and write a sentence describing what the set represents.

A)
B)
C)
D)

Question 60

In a survey of 18 college students, it was found that 11 were taking an English class, 6 were taking a
Math class, and 4 were taking both English and math. How many students were taking a math class
Only?

A)11
B)2
C)7
D)5

Question 61

The general term of the set is .

Question 62

Show that the set is an infinite set.

Question 63

Find the general term of the set.

Question 64

Find the general term of the set. {9, 12, 15, 18, 21, . . .}

A)
B)
C)
D)

Question 65

Which set is finite?

A){2, 4, 6, 8, 10, 12, . . .}
B)
C)
D)

Question 66

Show that the set is an infinite set. {0, 4, 8, 12, 16, . . .}

Question 67

Show that the given set is countable. {3, 6, 9, 12, 15, ...}

Question 68

Show that the set is an infinite set.

Question 69

Show that the set of positive rational numbers with denominators 3 or 5 is a countable set. (Rational
numbers are fractions with integers in the numerator and denominator.)

Question 70

Find the general term of the set. {-10, -20, -30, -40, -50, . . .}

A)-11n + 1
B)-9n - 1
C)-10n
D)n - 11

Question 71

Which set is infinite?

A)
B)
C){3, 5, 7, . . ., 99}
D)

Question 72

Show that the set is an infinite set. {6, 12, 18, 24, 30, . . .}

Question 73

Upon examining the contents of 38 backpacks, it was found that 23 contained a black pen, 27
Contained a blue pen, and 21 contained a pencil, 15 contained both a black pen and a blue pen, 12
Contained both a black pen and a pencil, 18 contained both a blue pen and a pencil, and 10 contained
All three items. How many backpacks contained exactly two of the three writing instruments?

A)11
B)2
C)15
D)3