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Applied Mathematics: For the Managerial, Life, and Social Sciences

Soo T. Tan

Chapter 7

Sets and Probability - all with Video Answers

Educators

Section 1

Sets and Set Operations

00:58

Problem 1

Write the set in set-builder notation.
The set of gold medalists in the 2010 Winter Olympic Games

AG
Ankit Gupta
Numerade Educator
00:27

Problem 2

Write the set in set-builder notation.
The set of football teams in the NFL

Mohamed Mohamed
Mohamed Mohamed
Numerade Educator
00:58

Problem 3

Write the set in set-builder notation.
$$
\{3,4,5,6,7\}
$$

AG
Ankit Gupta
Numerade Educator
00:58

Problem 4

Write the set in set-builder notation.
$$
\{1,3,5,7,9,11, \ldots, 39\}
$$

AG
Ankit Gupta
Numerade Educator
01:17

Problem 5

List the elements of the set in roster notation.
$$
\{x \mid x \text { is a digit in the number } 352,646\}
$$

Vysakh M
Vysakh M
Numerade Educator
01:17

Problem 6

List the elements of the set in roster notation.
$$
\{x \mid x \text { is a letter in the word HIPPOPOTAMUS }\}
$$

Vysakh M
Vysakh M
Numerade Educator
01:17

Problem 7

List the elements of the set in roster notation.
$$
\{x \mid 2-x=4 \text { and } x \text { is an integer }\}
$$

Vysakh M
Vysakh M
Numerade Educator
01:17

Problem 8

List the elements of the set in roster notation.
$$
\{x \mid 2-x=4 \text { and } x \text { is a fraction }\}
$$

Vysakh M
Vysakh M
Numerade Educator
00:12

Problem 9

State whether the statements are true or false.
a. $\{a, b, c\}=\{c, a, b\}$
b. $A \in A$

Rebecca Wang
Rebecca Wang
Numerade Educator
01:02

Problem 10

State whether the statements are true or false.
a. $\varnothing \in A$
b. $A \subset A$

Destin Priester
Destin Priester
Numerade Educator
00:41

Problem 11

State whether the statements are true or false.
a. $0 \in \varnothing$
b. $0=\varnothing$

Tanishq Gupta
Tanishq Gupta
Numerade Educator
00:41

Problem 12

State whether the statements are true or false.
a. $\{\varnothing\}=\varnothing$
b. $\{a, b\} \in\{a, b, c\}$

Tanishq Gupta
Tanishq Gupta
Numerade Educator
01:02

Problem 13

State whether the statements are true or false.
$$
\begin{array}{l}
\text { \{Chevrolet, Pontiac, Buick }\} \subset\{x \mid x \text { is a division of General }\\
\text { Motors\} }
\end{array}
$$

Destin Priester
Destin Priester
Numerade Educator
00:41

Problem 14

State whether the statements are true or false.
$$
\begin{array}{l}
\{x \mid x \text { is a silver medalist in the } 2010 \text { Winter Olympic }\\
\text { Games }\}=\varnothing
\end{array}
$$

Tanishq Gupta
Tanishq Gupta
Numerade Educator
00:18

Problem 15

Let $A=\{1,2,3,4,5\} .$ Determine whether the statements are true or false.
a. $2 \in A$
b. $A \subseteq\{2,4,6\}$

Amy Jiang
Amy Jiang
Numerade Educator
00:31

Problem 16

Let $A=\{1,2,3,4,5\} .$ Determine whether the statements are true or false.
a. $0 \in A$
b. $\{1,3,5\} \in A$

James Kiss
James Kiss
Numerade Educator
01:05

Problem 17

Let $A=\{1,2,3\}$. Which of the following sets are equal to $A$ ?
a. $\{2,1,3\}$
b. $\{3,2,1\}$
c. $\{0,1,2,3\}$

Manisha Sarker
Manisha Sarker
Numerade Educator
00:22

Problem 18

Let $A=\{a, e, l, t, r\} .$ Which of the following sets are equal to $A$ ?
a. $\{x \mid x$ is a letter of the word later\}
b. $\{x \mid x$ is a letter of the word latter $\}$
c. $\{x \mid x$ is a letter of the word relate $\}$

Elizabeth Xu
Elizabeth Xu
Numerade Educator
01:16

Problem 19

List all subsets of the following sets:
a. $\{1,2\}$
b. $\{1,2,3\}$
c. $\{1,2,3,4\}$

Heather Zimmers
Heather Zimmers
Numerade Educator
00:23

Problem 20

List all subsets of the set $A=\{\mathrm{IBM}$, U.S. Steel, Union Carbide, Boeing\}. Which of these are proper subsets of $A$ ?

Ashley Volpe
Ashley Volpe
Numerade Educator
01:10

Problem 21

Find the smallest possible set (i.e., the set with the least number of elements) that contains the given sets as subsets.
$$
\{1,2\},\{1,3,4\},\{4,6,8,10\}
$$

Aman Gupta
Aman Gupta
Numerade Educator
01:10

Problem 22

Find the smallest possible set (i.e., the set with the least number of elements) that contains the given sets as subsets.
$$
\{1,2,4\},\{a, b\}
$$

Aman Gupta
Aman Gupta
Numerade Educator
01:10

Problem 23

Find the smallest possible set (i.e., the set with the least number of elements) that contains the given sets as subsets.
$$
\text { \{Jill, John, Jack\}, \{Susan, Sharon\} }
$$

Aman Gupta
Aman Gupta
Numerade Educator
01:10

Problem 24

Find the smallest possible set (i.e., the set with the least number of elements) that contains the given sets as subsets.
$$
\begin{array}{l}
\text { \{GM, Ford, Chrysler\}, \{Daimler-Benz, Volkswagen\}, \{Toy- }\\
\text { ota, Nissan\} }
\end{array}
$$

Aman Gupta
Aman Gupta
Numerade Educator
00:47

Problem 25

Use Venn diagrams to represent the following relationships:
a. $A \subset B$ and $B \subset C$
b. $A \subset U$ and $B \subset U$, where $A$ and $B$ have no elements in
common
c. The sets $A, B$, and $C$ are equal.

Anthony Ramos
Anthony Ramos
Numerade Educator
01:18

Problem 26

Let $U$ denote the set of all students who applied for admission to the freshman class at Faber College for the upcoming academic year, and let
$A=\{x \in U \mid x$ is a successful applicant $\}$
$B=\{x \in U \mid x$ is a female student who enrolled in the freshman class\}
$C=\{x \in U \mid x$ is a male student who enrolled in the freshman class\}
a. Use Venn diagrams to represent the sets $U, A, B$, and $C$.
b. Determine whether the following statements are true or false.
i. $A \subseteq B$
ii. $B \subset A$
iii. $C \subset B$

Amy Jiang
Amy Jiang
Numerade Educator
00:44

Problem 27

Shade the portion of the accompanying figure that represents each set.
a. $A \cap B^{c}$
b. $A^{c} \cap B$

Amy Jiang
Amy Jiang
Numerade Educator
01:10

Problem 28

Shade the portion of the accompanying figure that represents each set.
a. $A^{c} \cap B^{c}$
b. $(A \cup B)^{c}$

Amy Jiang
Amy Jiang
Numerade Educator
01:54

Problem 29

Shade the portion of the accompanying figure that represents each set.
a. $A \cup B \cup C$
b. $A \cap B \cap C$

Maxime Rossetti
Maxime Rossetti
Numerade Educator
00:44

Problem 30

Shade the portion of the accompanying figure that represents each set.
a. $A \cap B \cap C^{c}$
b. $A^{c} \cap B \cap C$

Amy Jiang
Amy Jiang
Numerade Educator
01:10

Problem 31

Shade the portion of the accompanying figure that represents each set.
a. $A^{c} \cap B^{c} \cap C^{c}$
b. $(A \cup B)^{c} \cap C$

Amy Jiang
Amy Jiang
Numerade Educator
01:10

Problem 32

Shade the portion of the accompanying figure that represents each set.
a. $A \cup(B \cap C)^{c}$
b. $(A \cup B \cup C)^{c}$

Amy Jiang
Amy Jiang
Numerade Educator
01:07

Problem 33

Let $U=\{1,2,3,4,5,6,7,8,9,10\}$ $A=\{1,3,5,7,9\}, B=\{2,4,6,8,10\}$, and $C=\{1,2,4,$, $5,8,9\}$. List the elements of each set.
a. $A^{c}$
b. $B \cup C$
c. $C \cup C^{c}$

Manisha Sarker
Manisha Sarker
Numerade Educator
01:01

Problem 34

Let $U=\{1,2,3,4,5,6,7,8,9,10\}$ $A=\{1,3,5,7,9\}, B=\{2,4,6,8,10\}$, and $C=\{1,2,4,$, $5,8,9\}$. List the elements of each set.
a. $C \cap C^{c}$
b. $(A \cap C)^{c}$
c. $A \cup(B \cap C)$

Sanchit Jain
Sanchit Jain
Numerade Educator
01:23

Problem 35

Let $U=\{1,2,3,4,5,6,7,8,9,10\}$ $A=\{1,3,5,7,9\}, B=\{2,4,6,8,10\}$, and $C=\{1,2,4,$, $5,8,9\}$. List the elements of each set.
a. $(A \cap B) \cup C$
b. $(A \cup B \cup C)^{c}$
c. $(A \cap B \cap C)^{c}$

Manisha Sarker
Manisha Sarker
Numerade Educator
01:23

Problem 36

Let $U=\{1,2,3,4,5,6,7,8,9,10\}$ $A=\{1,3,5,7,9\}, B=\{2,4,6,8,10\}$, and $C=\{1,2,4,$, $5,8,9\}$. List the elements of each set.
a. $A^{c} \cap\left(B \cap C^{c}\right)$
b. $\left(A \cup B^{c}\right) \cup\left(B \cap C^{c}\right)$
c. $(A \cup B)^{c} \cap C^{c}$

Manisha Sarker
Manisha Sarker
Numerade Educator
View

Problem 37

Determine whether the pairs of sets are disjoint.
a. $\{1,2,3,4\},\{4,5,6,7\}$
b. $\{a, c, e, g\},\{b, d, f\}$

Nick Johnson
Nick Johnson
Numerade Educator
View

Problem 38

Determine whether the pairs of sets are disjoint.
a. $\varnothing,\{1,3,5\}$
b. $\{0,1,3,4\},\{0,2,5,7\}$

Nick Johnson
Nick Johnson
Numerade Educator
05:18

Problem 39

Let $U$ denote the set of all employees at Universal Life Insurance Company and let
$$
\begin{array}{l}
\boldsymbol{T}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { drinks tea }\} \\
\boldsymbol{C}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { drinks coffee }\}
\end{array}
$$
Describe each set in words.
a. $T^{c}$
b. $C^{c}$

Melissa Munoz
Melissa Munoz
Numerade Educator
05:18

Problem 40

Let $U$ denote the set of all employees at Universal Life Insurance Company and let
$$
\begin{array}{l}
\boldsymbol{T}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { drinks tea }\} \\
\boldsymbol{C}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { drinks coffee }\}
\end{array}
$$
Describe each set in words.
a. $T \cup C$
b. $T \cap C$

Melissa Munoz
Melissa Munoz
Numerade Educator
05:18

Problem 41

Let $U$ denote the set of all employees at Universal Life Insurance Company and let
$$
\begin{array}{l}
\boldsymbol{T}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { drinks tea }\} \\
\boldsymbol{C}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { drinks coffee }\}
\end{array}
$$
Describe each set in words.
a. $T \cap C^{c}$
b. $T^{c} \cap C$

Melissa Munoz
Melissa Munoz
Numerade Educator
05:18

Problem 42

Let $U$ denote the set of all employees at Universal Life Insurance Company and let
$$
\begin{array}{l}
\boldsymbol{T}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { drinks tea }\} \\
\boldsymbol{C}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { drinks coffee }\}
\end{array}
$$
Describe each set in words.
a. $T^{c} \cap C^{c}$
b. $(T \cup C)^{c}$

Melissa Munoz
Melissa Munoz
Numerade Educator
05:18

Problem 43

Let $U$ denote the set of all employees in a hospital. Let
$$
\begin{array}{l}
\boldsymbol{N}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a nurse }\} \\
\boldsymbol{D}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a doctor\} } \\
\boldsymbol{A}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is an administrator\} } \\
\boldsymbol{M}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a male\} } \\
\boldsymbol{F}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a female }\}
\end{array}
$$
Describe each set in words.
a. $D^{c}$
b. $N^{c}$

Melissa Munoz
Melissa Munoz
Numerade Educator
05:18

Problem 44

Let $U$ denote the set of all employees in a hospital. Let
$$
\begin{array}{l}
\boldsymbol{N}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a nurse }\} \\
\boldsymbol{D}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a doctor\} } \\
\boldsymbol{A}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is an administrator\} } \\
\boldsymbol{M}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a male\} } \\
\boldsymbol{F}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a female }\}
\end{array}
$$
Describe each set in words.
a. $N \cup D$
b. $N \cap M$

Melissa Munoz
Melissa Munoz
Numerade Educator
05:18

Problem 45

Let $U$ denote the set of all employees in a hospital. Let
$$
\begin{array}{l}
\boldsymbol{N}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a nurse }\} \\
\boldsymbol{D}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a doctor\} } \\
\boldsymbol{A}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is an administrator\} } \\
\boldsymbol{M}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a male\} } \\
\boldsymbol{F}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a female }\}
\end{array}
$$
Describe each set in words.
a. $D \cap M^{c}$
b. $D \cap A$

Melissa Munoz
Melissa Munoz
Numerade Educator
05:18

Problem 46

Let $U$ denote the set of all employees in a hospital. Let
$$
\begin{array}{l}
\boldsymbol{N}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a nurse }\} \\
\boldsymbol{D}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a doctor\} } \\
\boldsymbol{A}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is an administrator\} } \\
\boldsymbol{M}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a male\} } \\
\boldsymbol{F}=\{\boldsymbol{x} \in \boldsymbol{U} \mid \boldsymbol{x} \text { is a female }\}
\end{array}
$$
Describe each set in words.
a. $N \cap F$
b. $(D \cup N)^{c}$

Melissa Munoz
Melissa Munoz
Numerade Educator
04:48

Problem 47

Let $U$ denote the set of all senators in Congress and let
$$
\begin{array}{l}
D=\{x \in U \mid x \text { is a Democrat }\} \\
R=\{x \in U \mid x \text { is a Republican\} } \\
F=\{x \in U \mid x \text { is a female }\} \\
L=\{x \in U \mid x \text { is a lawyer }\}
\end{array}
$$
Write the set that represents each statement.
a. The set of all Democrats who are female
b. The set of all Republicans who are male and are not lawyers

Matthew Winsor
Matthew Winsor
Numerade Educator
04:48

Problem 48

Let $U$ denote the set of all senators in Congress and let
$$
\begin{array}{l}
D=\{x \in U \mid x \text { is a Democrat }\} \\
R=\{x \in U \mid x \text { is a Republican\} } \\
F=\{x \in U \mid x \text { is a female }\} \\
L=\{x \in U \mid x \text { is a lawyer }\}
\end{array}
$$
Write the set that represents each statement.
a. The set of all Democrats who are female or are lawyers
b. The set of all senators who are not Democrats or are
lawyers

Matthew Winsor
Matthew Winsor
Numerade Educator
View

Problem 49

Let $U$ denote the set of all students in the business college of a certain university. Let
$A=\{x \in U \mid x$ had taken a course in accounting $B=\{x \in U \mid x$ had taken a course in economics\}
$C=\{x \in U \mid x$ had taken a course in marketing $\}$
Write the set that represents each statement.
a. The set of students who have not had a course in economics
b. The set of students who have had courses in accounting and economics
c. The set of students who have had courses in accounting and economics but not marketing

Claire Rochford
Claire Rochford
Numerade Educator
View

Problem 50

Let $U$ denote the set of all students in the business college of a certain university. Let
$A=\{x \in U \mid x$ had taken a course in accounting $B=\{x \in U \mid x$ had taken a course in economics\}
$C=\{x \in U \mid x$ had taken a course in marketing $\}$
Write the set that represents each statement.
a. The set of students who have had courses in economics but not courses in accounting or marketing
b. The set of students who have had at least one of the
three courses
c. The set of students who have had all three courses

Claire Rochford
Claire Rochford
Numerade Educator
00:10

Problem 51

Refer to the following diagram, where $U$ is the set of all tourists surveyed over a 1-week period in London and where
$A=\{x \in U \mid x$ has taken the underground [subway]\}
$$
\begin{array}{l}
B=\{x \in U \mid x \text { has taken a cab }\} \\
C=\{x \in U \mid x \text { has taken a bus\} }
\end{array}
$$
Express the indicated regions in set notation and in words.
a. Region 1
b. Regions 1 and 4 together
c. Regions $4,5,7$, and 8 together

Coach Rye
Coach Rye
Numerade Educator
00:10

Problem 52

Refer to the following diagram, where $U$ is the set of all tourists surveyed over a 1-week period in London and where
$A=\{x \in U \mid x$ has taken the underground [subway]\}
$$
\begin{array}{l}
B=\{x \in U \mid x \text { has taken a cab }\} \\
C=\{x \in U \mid x \text { has taken a bus\} }
\end{array}
$$
Express the indicated regions in set notation and in words.
a. Region 3
b. Regions 4 and 6 together
c. Regions 5,6, and 7 together

Coach Rye
Coach Rye
Numerade Educator
02:04

Problem 53

Use Venn diagrams to illustrate each statement.
$$
A \subseteq A \cup B ; B \subseteq A \cup B \quad \text { 54. } A \cap B \subseteq A ; A \cap B \subseteq B
$$

Doruk Isik
Doruk Isik
Numerade Educator
01:21

Problem 54

Use Venn diagrams to illustrate each statement.
$$
A \cup(B \cup C)=(A \cup B) \cup C
$$

Laurie Huffman
Laurie Huffman
Numerade Educator
02:51

Problem 54

Use Venn diagrams to illustrate each statement.
$$
A \cap B \subseteq A ; A \cap B \subseteq B
$$

James Chok
James Chok
Numerade Educator
01:21

Problem 55

Use Venn diagrams to illustrate each statement.
$$
A \cup(B \cup C)=(A \cup B) \cup C
$$

Laurie Huffman
Laurie Huffman
Numerade Educator
02:51

Problem 56

Use Venn diagrams to illustrate each statement.
$$
A \cap(B \cap C)=(A \cap B) \cap C
$$

James Chok
James Chok
Numerade Educator
02:51

Problem 57

Use Venn diagrams to illustrate each statement.
$$
A \cap(B \cup C)=(A \cap B) \cup(A \cap C)
$$

James Chok
James Chok
Numerade Educator
01:55

Problem 58

Use Venn diagrams to illustrate each statement.
$$
(A \cup B)^{c}=A^{c} \cap B^{c}
$$

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
05:15

Problem 59

Let
$$
\begin{array}{l}
U=\{1,2,3,4,5,6,7,8,9,10\} \\
A=\{1,3,5,7,9\} \\
B=\{1,2,4,7,8\} \\
C=\{2,4,6,8\}
\end{array}
$$
Verify each equation by direct computation.
a. $A \cup(B \cup C)=(A \cup B) \cup C$
b. $A \cap(B \cap C)=(A \cap B) \cap C$

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
05:15

Problem 60

Let
$$
\begin{array}{l}
U=\{1,2,3,4,5,6,7,8,9,10\} \\
A=\{1,3,5,7,9\} \\
B=\{1,2,4,7,8\} \\
C=\{2,4,6,8\}
\end{array}
$$
Verify each equation by direct computation.
a. $A \cap(B \cup C)=(A \cap B) \cup(A \cap C)$
b. $(A \cup B)^{c}=A^{c} \cap B^{c}$

Himanshu Kushwaha
Himanshu Kushwaha
Numerade Educator
00:57

Problem 61

Refer to the accompanying figure and list the points that belong to each set.
a. $A \cup B$
b. $A \cap B$

Amy Jiang
Amy Jiang
Numerade Educator
01:10

Problem 62

Refer to the accompanying figure and list the points that belong to each set.
a. $A \cap(B \cup C)$
b. $(B \cap C)^{c}$

Amy Jiang
Amy Jiang
Numerade Educator
00:12

Problem 63

Refer to the accompanying figure and list the points that belong to each set.
a. $(B \cup C)^{c}$
b. $A^{c}$

Amy Jiang
Amy Jiang
Numerade Educator
01:10

Problem 64

Refer to the accompanying figure and list the points that belong to each set.
a. $(A \cap B) \cap C$
b. $(A \cup B \cup C)^{c}$

Amy Jiang
Amy Jiang
Numerade Educator
02:10

Problem 65

Suppose $A \subset B$ and $B \subset C$, where $A$ and $B$ are any two sets. What conclusion can be drawn regarding the sets $A$ and $C$ ?

Anthony Ramos
Anthony Ramos
Numerade Educator
04:11

Problem 66

Verify the assertion that two sets $A$ and $B$ are equal if and only if (1) $A \subseteq B$ and (2) $B \subseteq A$.

Anthony Ramos
Anthony Ramos
Numerade Educator
00:53

Problem 67

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
A set is never a subset of itself.

Destin Priester
Destin Priester
Numerade Educator
01:02

Problem 68

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
A proper subset of a set is itself a subset of the set but not necessarily vice versa.

Destin Priester
Destin Priester
Numerade Educator
00:25

Problem 69

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If $A \cup B=\varnothing$, then $A=\varnothing$ and $B=\varnothing$

Tanishq Gupta
Tanishq Gupta
Numerade Educator
00:25

Problem 70

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If $A \cap B=\varnothing$, then either $A=\varnothing$ or $B=\varnothing$

Tanishq Gupta
Tanishq Gupta
Numerade Educator
00:25

Problem 71

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
$$
\left(A \cup A^{c}\right)^{c}=\varnothing
$$

Tanishq Gupta
Tanishq Gupta
Numerade Educator
01:27

Problem 72

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
If $A \subseteq B$, then $A \cap B=A$.

Ahmad Reda
Ahmad Reda
Numerade Educator