MATH 132 University of Nevada Las Vegas Section 7 Universal Set Algebra Worksheet

10/11/21, 10:12 PMQuiz: Section 7.1
Section 7.1
Started: Oct 10 at 2:38pm
Quiz Instructions
Question 1
6 pts
Given the following sets:
U = {a, b, c, d, e, f , g, h}
A = {b, d, e, g, h}
;
B = {c, d, e, g}
;
C = {b, g, h}
and knowing that U is the Universal Set (i.e., the set of all elements under
consideration), answer the following questions. Enter your answers in the boxes
below as {a, b, c, d, e} with no space entered before or after each comma,
and numbers or letters should be entered in proper ascending order as shown
above.
a)
b)
c)
d)
¯
¯
¯
¯
¯
¯
¯
¯
A ∩ C =
(A ∪ B) ∩ (A ∪ C ) =
A ∪ (B ∩ C ) =
¯
¯
¯
¯
B ∩ C =
For the following questions, enter true or false, without capitalizing the first letter.
e)
Is
A ⊆ B
a true or a false statement?
f)
Is
B ⊆ C
a true or a false statement?
g)
Is
C ⊆ B
a true or a false statement?
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10/11/21, 10:12 PM
h)
Quiz: Section 7.1
Is
a true or a false statement?
C ⊆ A
Question 2
6 pts
Given the following sets:
U = {5, 6, 7, 8, 9, 30, 54, 68, 71}
A = {5, 9, 30, 71}
;
B = {7, 8, 9, 54, 68}
;
C = {9, 30}
and knowing that U is the Universal Set (i.e., the set of all elements under
consideration), answer the following questions. Enter your answers in the boxes
below as {a, b, c, d, e} with no space entered before or after each comma,
and numbers or letters should be entered in proper ascending order as shown
above.
a)
¯
¯
¯
¯
b)
¯
¯¯¯
¯¯¯
¯¯¯
¯¯
¯
c)
A ∪ C =
B ∩ A =
¯
¯¯
¯¯¯
¯¯¯
¯¯
¯
¯
A ∩ (B ∩ C) =
For the following questions, enter true or false, without capitalizing the first letter.
d)
Is
e)
Is
f)
Is
C ⊆ B
A ⊆ C
C ⊆ A
a true or a false statement?
a true or a false statement?
a true or a false statement?
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Quiz: Section 7.1
Question 3
6 pts
Given the following sets:
U = {1, 2, 3, 4, 5, 6}
A = {1, 2, 3}
;
and knowing that
B = {2, 3, 4}
U
;
C = {1, 5}
is the Universal Set (i.e., the set of all elements under
consideration), answer the following questions. Enter your answers in the boxes
below as {a, b, c, d, e} with no space entered before or after each comma,
and numbers or letters should be entered in proper ascending order as shown
above.
a)
b)
c)
d)
¯
¯¯¯
¯¯¯
¯¯¯¯
¯
¯
A ∪ C =
¯
¯
¯
¯
(B ∩ A) ∪ C =
¯
¯¯¯
¯¯¯
¯¯¯¯
¯
¯
C ∩ A =
A ∩ B =
For the following questions, enter true or false, without capitalizing the first letter.
e)
Is
A ⊆ B
a true or a false statement?
f)
Is
B ⊆ U
a true or a false statement?
g)
Is
B ⊆ A
a true or a false statement?
Question 4
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6 pts
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10/11/21, 10:12 PM
Quiz: Section 7.1
Given the following sets:
U = {3, 5, 7, 8, 9, 10, 11, 12, 13, 14, 16}
A = {3, 8, 9, 11, 14}
and knowing that
U
;
B = {3, 8, 9, 10, 11, 14, 16}
;
C = {3, 10}
is the Universal Set (i.e., the set of all elements under
consideration), answer the following questions. Enter your answer as
{a, b, c, d, e} with no space entered before or after each comma, and where
the letters represent appropriate set elements provided above.
a)
¯
¯¯¯
¯¯¯
¯¯¯¯
¯
¯
b)
¯
¯
¯
¯
c)
¯
¯¯
¯¯¯
¯¯¯
¯¯
¯
¯
d)
A ∪ C =
C ∩ (B ∩ A) =
B ∩ C =
¯
¯
¯
¯
A ∩ B =
For the following questions, enter true or false, without capitalizing the first letter.
e)
Is
A ⊆ B
a true or a false statement?
f)
Is
B ⊆ A
a true or a false statement?
g)
Is
B ⊆ U
a true or a false statement?
h)
Is
C ⊆ A
a true or a false statement?
i)
Is
C ⊆ B
a true or a false statement?
Question 5
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6 pts
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Quiz: Section 7.1
Given the following sets:
U = {1, 2, 3, 4, 5, 6}
A = {1, 2}
;
and knowing that
B = {2, 4, 5}
U
;
C = {1, 2, 5, 6}
is the Universal Set (i.e., the set of all elements under
consideration), answer the following questions. Enter your answers in the boxes
below as {a, b, c, d, e} with no space entered before or after each comma,
and numbers or letters should be entered in proper ascending order as shown
above.
a)
b)
A ∪ B =
A ∩ B =
c)
A ∩ C =
d)
B ∩ C =
e)
B ∪ C =
f)
¯
¯
¯
¯
A =
g)
¯
¯
¯
¯
h)
¯
¯
¯
¯
B =
C =
For the following questions, enter true or false, without capitalizing the first letter.
i)
Is
j)
Is
A ⊆ C
B ⊆ C
a true or a false statement?
a true or a false statement?
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Quiz: Section 7.1
Question 6
6 pts
Given the following sets:
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}
A = {1, 3, 5, 7}
and knowing that
and
U
B = {3, 4, 5, 6, 8, 10}
is the Universal Set (i.e., the set of all elements under
consideration), answer the following questions. Enter your answers in the boxes
below as {a, b, c, d, e} with no space entered before or after each comma,
and numbers or letters should be entered in proper ascending order as shown
above.
a)
b)
A ∪ B =
A ∩ B =
c)
¯
¯
¯
¯
d)
¯
¯
¯
¯
A =
B =
For the following questions, enter true or false, without capitalizing the first letter.
e)
Is
A ⊆ B
a true or a false statement?
f)
Is
B ⊆ A
a true or a false statement?
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Quiz: Section 7.2
Section 7.2
Started: Oct 10 at 2:39pm
Quiz Instructions
Question 1
Given
3 pts
137 , n (E) = 88 , n (F ) = 78 , calculate
and enter your answer in the box provided below.
n (E ∪ F ) =
n (E ∩ F ) =?
Question 2
Given
3 pts
13 , n (A) = 58 , n (B) = 96 , calculate
and enter your answer in the box provided below.
n (A ∩ B) =
n (A ∪ B) =?
Question 3
3 pts
After a survey of its employees, a car manufacturing company in Michigan discovers
that 1,338 of its employees own American model vehicles, 545 own Japanese
made vehicles, and 221 own both American and Japanese made vehicles. How
many employees of this car company own at least one of these makes of vehicles?
(Enter your answer in the box below).
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Quiz: Section 7.2
Question 4
3 pts
In a large residential neighborhood, 185 residents have desert landscaping to save
precious water, 102 residents have water-intensive landscaping, and 20 had a
mix of both desert type and water-intensive landscaping. How many residents in the
neighborhood have at least one of these types of landscaping? (Enter your answer
in the box below).
Question 5
6 pts
Consider the following Venn Diagram, depicting the data from a survey of customers
at a popular downtown Las Vegas restaurant about their favorite food.
a) How many customers selected only burger as their favorite food?
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Quiz: Section 7.2
b) How many customers selected both burger and pizza, but not spaghetti as their
favorite food?
c) How many customers selected burger and pizza as their favorite food?
d) How many customers did not select any of these three types of food as their
favorite item on the menu?
e) How many customers selected spaghetti and pizza, but not burger as their favorite
item on the menu?
f) How many customers selected only spaghetti as their favorite food?
Question 6
6 pts
Consider the following Venn Diagram, depicting the data from a survey of college
students who were asked if they spoke another language than English, fluently.
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Quiz: Section 7.2
a) How many students spoke both French and German fluently?
b) How many students spoke only French fluently?
c) How many students spoke Spanish fluently?
d) How many students spoke both Spanish and German, but not French?
e) How many students spoke both French and Spanish, but not German?
f) How many students spoke only German?
Question 7
6 pts
Consider the following Venn Diagram, depicting the data from surveying random
individuals passing by on the street at a neighborhood in Chicago about what second
language (other than English) they could speak.
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Quiz: Section 7.2
a) How many passersby could speak only Russian as a second language?
b) How many passersby could speak all three languages as the second language?
c) How many passersby could speak both Chinese and Spanish as the second
language, but not Russian?
d) How many passersby could speak Chinese as the second language?
e) How many passersby could speak either Chinese or Russian as the second
language, or both Chinese and Russian, but no Spanish at all?
f) How many passersby could speak Spanish as the second language?
Question 8
5 pts
A group of 65 students were surveyed about whether or not they liked any or all of
three kinds of fruits: apricots, bananas, and cantaloupes. It was found that:
34
liked apricots
30
liked bananas
33
liked cantaloupes
11
liked apricots and bananas
15
liked bananas and cantaloupes
17
liked apricots and cantaloupes
7
liked all the three fruits
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Quiz: Section 7.2
Which of the following Venn diagrams is an accurate depiction of the above
information?
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Quiz: Section 7.2
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Quiz: Section 7.2
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Quiz: Section 7.2
Question 9
5 pts
A pet store keeps track of the purchases over a four hour period. The store manager
classifies purchases as containing a dog product, a cat product, a fish product, or
product for a different kind of pet. She found:
83
101
purchased a dog product
purchased a cat product
22
purchased a fish product
31
purchased a dog and a cat product
8
10
6
34
purchased a dog and a fish product
purchased a cat and a fish product
purchased a dog, a cat, and a fish product
purchased a product for a pet other than a dog, cat, or fish
Select the Venn Diagram below that best depicts the above information.
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Quiz: Section 7.2
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Quiz: Section 7.2
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Quiz: Section 7.2
Question 10
A survey of
109
94
218
5 pts
UNLV students during the fall semester revealed that:
had Facebook accounts
had Instagram accounts
86
had Twitter accounts
47
had both Facebook & Twitter accounts
25
had both Instagram & Twitter accounts
39
had both Facebook & Instagram accounts
23
17
had all three social media accounts
did not have any of these social media accounts
Which diagram below is an accurate Venn diagram for the above information?
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Quiz: Section 7.2
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Quiz: Section 7.2
Correct Venn diagram is not listed
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Quiz: Section 7.2
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