Deck 4: Sets and Algebra

Question 1

Let U = {Astros, Athletics, Giants, Mariners, Orioles, Pirates, Reds, Royals, Tigers}
A = {Athletics, Giants, Reds, Royals}
B = {Astros, Athletics, Giants, Royals, Tigers}
Find the following:

Answer 1

{Athletics, Giants, Royals}

Question 2

Which of the following are subsets of the set S, where S = {1, 3, 9, 27, …}?
{1, 27, 729}

Answer 2

Subset

Question 3

Which of the following are subsets of the set S, where S = {1, 3, 9, 27, …}?

Answer 3

{0, 3, 5, 7}

Question 4

Assume there are 25 students taking a computer class,
16 students taking an algebra class, and 32 students
taking at least one of the two classes. How many students
are taking both a computer class and an algebra class?
Fill in the Venn diagram below to illustrate your solution.

Question 5

Use set notation to represent each of the following.
The universal set of positive odd numbers.

Question 6

Which of the following are subsets of the set S, where S = {1, 3, 9, 27, …}?
{3, 27, 243, …}

Question 7

Which of the following are subsets of the set S, where S = {1, 3, 9, 27, …}?
{9, 81, 512}
Let U = {0, 1, 2, 3, 4, 5, 6, 7}
A = {0, 3, 6, 7}
B = {1, 2, 4, 6}

Question 8

Which of the following are subsets of the set S, where S = {1, 3, 9, 27, …}?

Question 9

Assume there are 25 students taking a computer class,
16 students taking an algebra class, and 32 students
taking at least one of the two classes. How many students
are taking both a computer class and an algebra class?
Fill in the Venn diagram below to illustrate your solution.

Question 10

Let U = {Astros, Athletics, Giants, Mariners, Orioles, Pirates, Reds, Royals, Tigers}
A = {Athletics, Giants, Reds, Royals}
B = {Astros, Athletics, Giants, Royals, Tigers}
Find the following:

Question 11

Let U = {Astros, Athletics, Giants, Mariners, Orioles, Pirates, Reds, Royals, Tigers}
A = {Athletics, Giants, Reds, Royals}
B = {Astros, Athletics, Giants, Royals, Tigers}
Find the following:
Let A = {students taking a computer class} 15.
B = {students taking an algebra class}

Question 12

Use set notation to represent each of the following.
The set of letters in the word bamboozle.

Question 13

Draw a Venn diagram for which the given cardinalities apply.

Question 14

Which of the following are subsets of the set S, where S = {1, 3, 9, 27, …}?

Question 15

Let U = {Astros, Athletics, Giants, Mariners, Orioles, Pirates, Reds, Royals, Tigers}
A = {Athletics, Giants, Reds, Royals}
B = {Astros, Athletics, Giants, Royals, Tigers}
Find the following:

Question 16

For each of the following propositions, find a negation.
Roses are red.

Question 17

Describe an element in the set

Question 18

Which of the following are subsets of the set S, where S = {1, 3, 9, 27, …}?

Question 19

Which of the following are subsets of the set S, where S = {1, 3, 9, 27, …}?
Shade the specified region on the following Venn diagram.

Question 20

Let U = {Astros, Athletics, Giants, Mariners, Orioles, Pirates, Reds, Royals, Tigers}
A = {Athletics, Giants, Reds, Royals}
B = {Astros, Athletics, Giants, Royals, Tigers}
Find the following:
Label the following regions on the Venn diagram below:
Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 4, 7, 8, 9}
B = {2, 3, 4, 5, 6, 9}

Question 21

Let U = {0, 1, 2, 3, 4, 5, 6, 7, A, B}
A = {0, 5, 6, B}
B = {1, 5, 7, A}
Find the following:

Question 22

Use set notation to represent each of the following.
The set of lowercase letters in the English alphabet.

Question 23

Use set notation to represent each of the following.
{5, 17, 29, …}

Question 24

Let U = {Bruins, Capitals, Flyers, Hurricanes, Lightning, Oilers, Panthers, Rangers}
A = {Flyers, Hurricanes, Lightning, Rangers}
B = {Bruins, Flyers, Hurricanes, Oilers, Panthers}
Find the following:
Label the following regions on the Venn diagram below:
Let U = {a, b, c, d, e, f, g, h, i, j}
A = {a, c, e, i}
B = {b, c, d, f, i}

Question 25

Jam is not jelly.

Question 26

Complete the following truth table. Identify the last 25.
column in the table as a condition statement, a fallacy,
or a tautology.

Question 27

Let U = {Bruins, Capitals, Flyers, Hurricanes, Lightning, Oilers, Panthers, Rangers}
A = {Flyers, Hurricanes, Lightning, Rangers}
B = {Bruins, Flyers, Hurricanes, Oilers, Panthers}
Find the following:

Question 28

Use set notation to represent each of the following.
The universal set of negative numbers.
Which of the following are subsets of the set R, where R = {1, 5, 9, 13, 17, …}?

Question 29

Let U = {Bruins, Capitals, Flyers, Hurricanes, Lightning, Oilers, Panthers, Rangers}
A = {Flyers, Hurricanes, Lightning, Rangers}
B = {Bruins, Flyers, Hurricanes, Oilers, Panthers}
Find the following:

Question 30

Let U = {Bruins, Capitals, Flyers, Hurricanes, Lightning, Oilers, Panthers, Rangers}
A = {Flyers, Hurricanes, Lightning, Rangers}
B = {Bruins, Flyers, Hurricanes, Oilers, Panthers}
Find the following:
Let A = {students taking a Spanish class} 15.
B = {students taking a judo class}
Assume there are 41 students taking a Spanish class,
22 students taking a judo class, and 8 students taking
both classes. How many students are taking at least
one of the two classes? Fill in the Venn diagram below
to illustrate your solution.

Question 31

Use set notation to represent each of the following.
{1, 21, 41}

Question 32

Question 33

How many computers have a DSL modem, an Ethernet
card, and Firewire ports?

Question 34

Let U = {0, 1, 2, 3, 4, 5, 6, 7, A, B}
A = {0, 5, 6, B}
B = {1, 5, 7, A}
Find the following:

Question 35

Use set notation to represent each of the following.
{9, 41, 75}

Question 36

Let U = {0, 1, 2, 3, 4, 5, 6, 7, A, B}
A = {0, 5, 6, B}
B = {1, 5, 7, A}
Find the following:
Shade the specified region on the following Venn diagram.

Question 37

Let U = {0, 1, 2, 3, 4, 5, 6, 7, A, B}
A = {0, 5, 6, B}
B = {1, 5, 7, A}
Find the following:

Question 38

Which of the following are propositions?

Question 39

Let U = {Bruins, Capitals, Flyers, Hurricanes, Lightning, Oilers, Panthers, Rangers}
A = {Flyers, Hurricanes, Lightning, Rangers}
B = {Bruins, Flyers, Hurricanes, Oilers, Panthers}
Find the following:

Question 40

Let U = {0, 1, 2, 3, 4, 5, 6, 7, A, B}
A = {0, 5, 6, B}
B = {1, 5, 7, A}
Find the following:

Question 41

For each of the following propositions, find a negation.
How many cars have a CD changer and airbags, but no
antilock brakes?

Question 42

For each of the following propositions, find a negation.
Which of the following are propositions?

Question 43

For each of the following propositions, find a negation.
Draw a Venn diagram for which the given cardinalities apply.

Question 44

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 8, 9}
B = {1, 3, 6, 7, 8}
C = {5, 6, 7, 8, 9}
Find the following:
BC∪ ′
(a) {1, 3}
(b) {1, 2, 5, 6, 7, 8, 9}
(c) {0, 1, 2, 3, 4, 5, 6, 7, 8}
(d) {1, 2, 3, 6, 7, 8}
(e) None of these

Question 45

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 8, 9}
B = {1, 3, 6, 7, 8}
C = {5, 6, 7, 8, 9}
Find the following:

(e) None of these

Question 46

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 8, 9}
B = {1, 3, 6, 7, 8}
C = {5, 6, 7, 8, 9}
Find the following:

(a) {5, 6, 7, 8, 9}
(b) {3, 4, 5, 6, 7}
(c) {0, 1, 2, 3, 4}
(d) {1, 2, 3, 4}
(e) None of these

Question 47

Use set notation to represent each of the following.
Which of the following is a subset of the set Q, where 3. Q = {1, 4, 16, 64, …}?
(a) {1, 4, 258}
(b) {1024, 4096}
(c) {128, 512, 2048}
(d) {16, 64, 384}
(e) None of these

Question 48

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 8, 9}
B = {1, 3, 6, 7, 8}
C = {5, 6, 7, 8, 9}
Find the following:

(a) {5, 6, 7, 8}
(b) {6, 7, 8}
(c) {1, 3, 5, 6, 7, 8, 9}
(d) {0, 6, 7, 8}
(e) None of these

Question 49

For each of the following propositions, find a negation.

Question 50

For each of the following propositions, find a negation.
Violets are Blue.
Let C = {cars with a CD changer}, with C = 24
B = {cars with antilock brakes}, with B = 58
A = {cars with airbags}, with A = 75

Question 51

For each of the following propositions, find a negation.
Describe an element in the set

Question 52

For each of the following propositions, find a negation.
Complete the following truth table. Identify the last 25.
column in the table as a condition statement, a fallacy,
or a tautology.

Question 53

For each of the following propositions, find a negation.
Go to the store.

Question 54

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 8, 9}
B = {1, 3, 6, 7, 8}
C = {5, 6, 7, 8, 9}
Find the following:

(a) {8, 9}
(b) {1, 2, 5, 6, 7, 8, 9}
(c) {1, 8}
(d) {1, 2, 3, 6, 7, 8, 9}
(e) None of these

Question 55

For each of the following propositions, find a negation.

Question 56

Use set notation to represent each of the following.
The universal set of U.S. states that border the Pacific Ocean.
(a) {California, Oregon, Washington}
(b) {Alaska, California, Oregon, Washington}
(c) {Alaska, California, Hawaii, Oregon, Washington}
(d) {Alaska, Arizona, California, Hawaii, Oregon, Washington}
(e) None of these

Question 57

Let U = {Bruins, Capitals, Flyers, Hurricanes, Lightning, Oilers, Panthers, Rangers}
A = {Flyers, Hurricanes, Lightning, Rangers}
B = {Bruins, Flyers, Hurricanes, Oilers, Panthers}
Find the following:

Question 58

Use set notation to represent each of the following.
The set of letters in the word porcupine.
(a) {p, o, r, c, u, p, i, n, e}
(b) {c, e, i, n, o, p, r, u}
(c) {c, e, i, n, p, r, u}
(d) {p, o, n, r, e, i, c}
(e) None of these

Question 59

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 8, 9}
B = {1, 3, 6, 7, 8}
C = {5, 6, 7, 8, 9}
Find the following:

(a) 3
(b) 4
(c) 5
(d) 6
(e) None of these

Question 60

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
A = {1, 2, 8, 9}
B = {1, 3, 6, 7, 8}
C = {5, 6, 7, 8, 9}
Find the following:

(a) 4
(b) 5
(c) 2
(d) 7
(e) None of these

Question 61

How many pizzas have either pepperoni, mushrooms, or olives?
(a) 16
(b) 3
(c) 17
(d) 19
(e) None of these

Question 62

Let U = {Bucks, Bulls, Celtics, Heat, Hornets, Jazz, Pistons,
Spurs, Pacers, Warriors, Wizards}
A = {Celtics, Heat, Jazz, Pacers, Warriors, Wizards}
B = {Bucks, Bulls, Celtics, Heat, Hornets, Wizards}
Find the following:

(a) {Bucks, Bulls, Celtics, Heat, Hornets, Jazz, Pacers, Warriors, Wizards}
(b) {Celtics, Heat, Wizards}
(c) {Heat, Wizards}
(d) {Bucks, Bulls, Celtics, Heat, Jazz, Pacers, Warriors, Wizards}
(e) None of these

Question 63

For each of the following propositions, find a negation.
124 Instructor's Resource Guide Mathematics for New Technologies

Question 64

Describe an element in the set
(a) Pizza with pepperoni or mushrooms
(b) Pizza with pepperoni and olives
(c) Pizza with pepperoni and mushrooms or olives
(d) Pizza with pepperoni or mushrooms or olives
(e) None of these

Question 65

Let U = {Bucks, Bulls, Celtics, Heat, Hornets, Jazz, Pistons,
Spurs, Pacers, Warriors, Wizards}
A = {Celtics, Heat, Jazz, Pacers, Warriors, Wizards}
B = {Bucks, Bulls, Celtics, Heat, Hornets, Wizards}
Find the following:

(a) 128
(b) 130
(c) 132
(d) 134
(e) None of these

Question 66

In the truth table below, is the last column in the table
(a) a condition statement,
(b) a fallacy,
(c) a tautology,
(d) or none of these?

Question 67

Which of the following is a proposition?
(a) Leave me alone.
(b) Why does it rain?
(c) The universe is big.
(d) Where did she go?
(e) None of these

Question 68

Let U = {Bucks, Bulls, Celtics, Heat, Hornets, Jazz, Pistons,
Spurs, Pacers, Warriors, Wizards}
A = {Celtics, Heat, Jazz, Pacers, Warriors, Wizards}
B = {Bucks, Bulls, Celtics, Heat, Hornets, Wizards}
Find the following:

(a) 3
(b) 4
(c) 5
(d) 6
(e) None of these

Question 69

Let U = {Bucks, Bulls, Celtics, Heat, Hornets, Jazz, Pistons,
Spurs, Pacers, Warriors, Wizards}
A = {Celtics, Heat, Jazz, Pacers, Warriors, Wizards}
B = {Bucks, Bulls, Celtics, Heat, Hornets, Wizards}
Find the following:
Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} 15. A = {1, 4, 7, 8, 9}
B = {2, 3, 4, 5, 6, 9}
Choose the correct Venn diagram.

Question 70

Which is the correct Venn diagram for the given cardinalities?
(e) None of these

Question 71

For each of the following propositions, find a negation.
The earth is flat.
(a) The earth is round.
(b) The earth is always flat.
(c) The flat is earth.
(d) The earth is not flat.
(e) None of these

Question 72

Evaluate
(a) 0
(b) 1

Question 73

Let U = {Bucks, Bulls, Celtics, Heat, Hornets, Jazz, Pistons,
Spurs, Pacers, Warriors, Wizards}
A = {Celtics, Heat, Jazz, Pacers, Warriors, Wizards}
B = {Bucks, Bulls, Celtics, Heat, Hornets, Wizards}
Find the following:

Question 74

Let U = {Bucks, Bulls, Celtics, Heat, Hornets, Jazz, Pistons,
Spurs, Pacers, Warriors, Wizards}
A = {Celtics, Heat, Jazz, Pacers, Warriors, Wizards}
B = {Bucks, Bulls, Celtics, Heat, Hornets, Wizards}
Find the following:

(a) 5
(b) 4
(c) 3
(d) 2
(e) None of these

Question 75

Let U = {Bucks, Bulls, Celtics, Heat, Hornets, Jazz, Pistons,
Spurs, Pacers, Warriors, Wizards}
A = {Celtics, Heat, Jazz, Pacers, Warriors, Wizards}
B = {Bucks, Bulls, Celtics, Heat, Hornets, Wizards}
Find the following:
Let A = {students taking a German class} 16. B = {students taking a philosophy class}
Assume there are 28 students taking a German class,
34 students taking a philosophy class, and 56 students
Taking at least one of the two classes. How many students
Are taking both a German class and a philosophy class?
(a) 5
(b) 6
(c) 7
(d) 8
(e) None of these