Question 1

Find the number of proper subsets of the set.
-$\{ x \mid x$ is a day of the week $\}$

Accepted Answer

A)  128 
B)  64 
C)  127 
D)  256 
A)  128 
B)  64 
C)  127 
D)  256

Question 2

Determine whether the statement is true or false. 
Let $A = \{ 1,3,5,7 \}$
$\begin{array} { l } 
B = \{ 5,6,7,8 \} \
C = \{ 5,8 \} \
D = \{ 2,5,8 \} \
U = \{ 1,2,3,4,5,6,7,8 \}
\end{array}$
-$C \subset D$

Accepted Answer

A) True 
 B)False

Question 3

List the elements in the set.
-The set of the days of the week

Accepted Answer

A)  {Tuesday, Thursday} 
B)  {Friday, Monday, Saturday, Sunday, Thursday, Tuesday, Wednesday} 
C)  {Saturday, Sunday } 
D)  {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} 
A)  {Tuesday, Thursday} 
B)  {Friday, Monday, Saturday, Sunday, Thursday, Tuesday, Wednesday} 
C)  {Saturday, Sunday } 
D)  {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday}

Question 4

Find the cardinal number of the set.
-The numbers in the Venn Diagram below represent cardinalities.  
Find $n ( B \cup C )$

Accepted Answer

A)  49 
B)  14 
C)  60 
D)  42 
A)  49 
B)  14 
C)  60 
D)  42

Question 5

Decide whether the given statement is always true or not always true.
-$( \mathrm { A } \cup \mathrm { B } ) ^ { \prime } = \mathrm { A } ^ { \prime } \cup \mathrm { B } ^ { \prime }$

Accepted Answer

A)  Not always true 
B)  Always true 
A)  Not always true 
B)  Always true

Question 6

List the elements in the set . Let
$\begin{array} { l } 
\mathrm { U } = \{ \mathrm { q } , \mathbf { r } , \mathrm { s } , \mathrm { t } , \mathbf { u } , \mathrm { v } , \mathbf { w } , \mathbf { x } , \mathrm { y } , \mathrm { z } \} \
\mathrm { A } = \{ \mathrm { q } , \mathrm { s } , \mathrm { u } , \mathbf { w } , \mathrm { y } \} \
\mathrm { B } = \{ \mathrm { q } , \mathrm { s } , \mathrm { y } , \mathrm { z } \} \
\mathrm { C } = \{ \mathrm { v } , \mathbf { w } , \mathbf { x } , \mathrm { y } , \mathrm { z } \}
\end{array}$
-$\left( A \cup B ^ { \prime } \right) ^ { \prime } \cap C ^ { \prime }$

Accepted Answer

A)  $\{ \mathrm { q } , \mathrm { r } , \mathrm { s } , \mathrm { t } , \mathrm { u } , \mathrm { z } \}$ 
B)  $\varnothing$ 
C)  $\{ \mathrm { q } , \mathrm { r } , \mathrm { s } , \mathrm { t } , \mathrm { u } \}$ 
D)  $\{ v , w , x , y \}$ 
A)  $\{ \mathrm { q } , \mathrm { r } , \mathrm { s } , \mathrm { t } , \mathrm { u } , \mathrm { z } \}$ 
B)  $\varnothing$ 
C)  $\{ \mathrm { q } , \mathrm { r } , \mathrm { s } , \mathrm { t } , \mathrm { u } \}$ 
D)  $\{ v , w , x , y \}$

Question 7

Find the indicated cardinal number.
-Find $n ( A )$ given that $n ( A \times B ) = 36$ and $n ( B ) = 3$.

Accepted Answer

A)  12 
B)  3 
C)  39 
D)  33 
A)  12 
B)  3 
C)  39 
D)  33

Question 8

Show that the set has cardinal number    by establishing a one-to-one correspondence between the set of counting numbers and the given set. Be sure to show the pairing of the general terms in the sets.
-$\left\{ \frac { 1 } { 4 } , \frac { 1 } { 5 } , \frac { 1 } { 6 } , \frac { 1 } { 7 } , \ldots \right\}$

Accepted Answer

A)  
  
B) 
  
C)  
  
D) 
  
A)  
  
B) 
  
C)  
  
D)

Question 9

Identify the set as finite or infinite.
-$\{ x \mid x$ is a prime number $\}$

Accepted Answer

A)  Infinite 
B)  Finite 
A)  Infinite 
B)  Finite

Question 10

Write true or false for the following statement. Let
$\begin{array} { l } 
A = \{ 3,5,7,9,11,13 \} \
B = \{ 3,5,9,11 \} \
C = \{ 5,9,13 \}
\end{array}$
-$0 \in A$

Accepted Answer

A) True 
 B)False

Question 11

Complete the blank with either $\in$ or $\notin$ to make the statement true.
-$9 \ldots \{ 4,5,6 , \ldots , 9 \}$

Accepted Answer

A)  $\in$ 
B)  $\notin$ 
A)  $\in$ 
B)  $\notin$

Question 12

Show that the set has cardinal number    by establishing a one-to-one correspondence between the set of counting numbers and the given set. Be sure to show the pairing of the general terms in the sets.
-$\left\{ \frac { 1 } { 2 } , \frac { 1 } { 6 } , \frac { 1 } { 18 } , \frac { 1 } { 54 } , \ldots \right\}$

Accepted Answer

A)  
  
B) 
  
C)  
  
D)  
  
A)  
  
B) 
  
C)  
  
D)

Question 13

Find the cardinal number of the set.
-Given: 
$\mathrm { n } ( \mathrm { A } \cup \mathrm { B } \cup \mathrm { C } ) = 69$
$\mathrm { n } ( \mathrm { A } \cap \mathrm { B } \cap \mathrm { C } ) = 10$
$\mathrm { n } ( \mathrm { A } \cap \mathrm { B } ) = 22$
$\mathrm { n } ( \mathrm { A } \cap \mathrm { C } ) = 19$
$\mathrm { n } ( \mathrm { B } \cap \mathrm { C } ) = 17$
$\mathrm { n } ( \mathrm { A } ) = 51$
$\mathrm { n } ( \mathrm { B } ) = 34$
$\mathrm { n } ( \mathrm { C } ) = 32$
Find $n \left( A ^ { \prime } \cap B \cap C \right)$

Accepted Answer

A)  6 
B)  7 
C)  8 
D)  9 
A)  6 
B)  7 
C)  8 
D)  9

Question 14

Shade the regions representing the set.
-$A ^ { \prime } \cup B ^ { \prime }$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 15

Tell whether the statement is true or false.
-$\mathrm { k } \notin \{ p , a , k , h , v \}$

Accepted Answer

A) True 
 B)False

Question 16

Write a description of the shaded region using the symbols A, B, C,  $\cup$,  $\cap$, -, and ' as needed.
-

Accepted Answer

A)  $( A \cap B ) \cap C ^ { \prime }$ 
B)  $( A \cup B ) \cup C ^ { \prime }$ 
C)  $( A \cup B ) \cap C$ 
D)  $( A \cup B ) \cap C ^ { \prime }$ 
A)  $( A \cap B ) \cap C ^ { \prime }$ 
B)  $( A \cup B ) \cup C ^ { \prime }$ 
C)  $( A \cup B ) \cap C$ 
D)  $( A \cup B ) \cap C ^ { \prime }$

Question 17

Write the set in set-builder notation.
-$\{ \ldots , - 3 , - 2 , - 1,0,1,2,3 , \ldots \}$

Accepted Answer

A)  $\{ - 3 , - 2 , - 1,0,1,2,3 \}$ 
B)  $\{ x \mid x$ is a natural number $\}$ 
C)  $\{ x \mid x$ is any integer greater than $- 3 \}$ 
D)  $\{ x \mid x$ is an integer $\}$ 
A)  $\{ - 3 , - 2 , - 1,0,1,2,3 \}$ 
B)  $\{ x \mid x$ is a natural number $\}$ 
C)  $\{ x \mid x$ is any integer greater than $- 3 \}$ 
D)  $\{ x \mid x$ is an integer $\}$

Question 18

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

Accepted Answer

A)  $\{ x \mid x$ is an odd integer greater than $- 4 \}$ 
B)  $\{ x \mid x$ is an odd integer between $- 4$ and $6 \}$ 
C)  $\{ x \mid x$ is an odd integer $\}$ 
D)  $\{ x \mid x$ is an integer greater than $- 4 \}$ 
A)  $\{ x \mid x$ is an odd integer greater than $- 4 \}$ 
B)  $\{ x \mid x$ is an odd integer between $- 4$ and $6 \}$ 
C)  $\{ x \mid x$ is an odd integer $\}$ 
D)  $\{ x \mid x$ is an integer greater than $- 4 \}$

Question 19

Shade the regions representing the set.
-$\left( A \cap B \cap C ^ { \prime } \right) ^ { \prime }$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 20

Write the set in set-builder notation.
-The set of all calculus books

Accepted Answer

A)  {any calculus book} 
B)  $\{ x \mid x$ is a calculus book $\}$ 
C)  $\{ x$ is a calculus book $\}$ 
D)  {a calculus book } 
A)  {any calculus book} 
B)  $\{ x \mid x$ is a calculus book $\}$ 
C)  $\{ x$ is a calculus book $\}$ 
D)  {a calculus book }

Find the number of proper subsets of the set. - $\{ x \mid x$ is a day of the week $\}$

Determine whether the statement is true or false. Let $A = \{ 1,3,5,7 \}$ B=\{5,6,7,8\} C=\{5,8\} D=\{2,5,8\} U=\{1,2,3,4,5,6,7,8\} - $C \subset D$

List the elements in the set. -The set of the days of the week

Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. $Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. Find n ( B \cup C )$ Find $n ( B \cup C )$

Decide whether the given statement is always true or not always true. - $( \mathrm { A } \cup \mathrm { B } ) ^ { \prime } = \mathrm { A } ^ { \prime } \cup \mathrm { B } ^ { \prime }$

List the elements in the set . Let =\{,,,,,,,,,\} =\{,,,,\} =\{,,,\} =\{,,,,\} - $\left( A \cup B ^ { \prime } \right) ^ { \prime } \cap C ^ { \prime }$

Find the indicated cardinal number. -Find $n ( A )$ given that $n ( A \times B ) = 36$ and $n ( B ) = 3$ .

Identify the set as finite or infinite. - $\{ x \mid x$ is a prime number $\}$

Write true or false for the following statement. Let A=\{3,5,7,9,11,13\} B=\{3,5,9,11\} C=\{5,9,13\} - $0 \in A$

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $9 \ldots \{ 4,5,6 , \ldots , 9 \}$

Shade the regions representing the set. - $A ^ { \prime } \cup B ^ { \prime }$ $Shade the regions representing the set. - A ^ { \prime } \cup B ^ { \prime }$

Tell whether the statement is true or false. - $\mathrm { k } \notin \{ p , a , k , h , v \}$

Write a description of the shaded region using the symbols A, B, C, $\cup$ , $\cap$ , -, and ' as needed. - $Write a description of the shaded region using the symbols A, B, C, \cup , \cap , -, and ' as needed. -$

Write the set in set-builder notation. - $\{ \ldots , - 3 , - 2 , - 1,0,1,2,3 , \ldots \}$

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

Shade the regions representing the set. - $\left( A \cap B \cap C ^ { \prime } \right) ^ { \prime }$ $Shade the regions representing the set. - \left( A \cap B \cap C ^ { \prime } \right) ^ { \prime }$

Write the set in set-builder notation. -The set of all calculus books

The Art of Problem Solving

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Exam 2: The Basic Concepts of Set Theory

Find the number of proper subsets of the set. - {x∣x\{ x \mid x{x∣x is a day of the week }\}}

Determine whether the statement is true or false. Let A={1,3,5,7}A = \{ 1,3,5,7 \}A={1,3,5,7} B=\{5,6,7,8\} C=\{5,8\} D=\{2,5,8\} U=\{1,2,3,4,5,6,7,8\} - C⊂DC \subset DC⊂D

List the elements in the set. -The set of the days of the week

Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. Find n(B∪C)n ( B \cup C )n(B∪C)

Decide whether the given statement is always true or not always true. - (A∪B)′=A′∪B′( \mathrm { A } \cup \mathrm { B } ) ^ { \prime } = \mathrm { A } ^ { \prime } \cup \mathrm { B } ^ { \prime }(A∪B)′=A′∪B′

List the elements in the set . Let =\{,,,,,,,,,\} =\{,,,,\} =\{,,,\} =\{,,,,\} - (A∪B′)′∩C′\left( A \cup B ^ { \prime } \right) ^ { \prime } \cap C ^ { \prime }(A∪B′)′∩C′

Find the indicated cardinal number. -Find n(A)n ( A )n(A) given that n(A×B)=36n ( A \times B ) = 36n(A×B)=36 and n(B)=3n ( B ) = 3n(B)=3 .

Identify the set as finite or infinite. - {x∣x\{ x \mid x{x∣x is a prime number }\}}

Write true or false for the following statement. Let A=\{3,5,7,9,11,13\} B=\{3,5,9,11\} C=\{5,9,13\} - 0∈A0 \in A0∈A

Complete the blank with either ∈\in∈ or ∉\notin∈/ to make the statement true. - 9…{4,5,6,…,9}9 \ldots \{ 4,5,6 , \ldots , 9 \}9…{4,5,6,…,9}

Shade the regions representing the set. - A′∪B′A ^ { \prime } \cup B ^ { \prime }A′∪B′

Tell whether the statement is true or false. - k∉{p,a,k,h,v}\mathrm { k } \notin \{ p , a , k , h , v \}k∈/{p,a,k,h,v}

Write a description of the shaded region using the symbols A, B, C, ∪\cup∪ , ∩\cap∩ , -, and ' as needed. -

Write the set in set-builder notation. - {…,−3,−2,−1,0,1,2,3,…}\{ \ldots , - 3 , - 2 , - 1,0,1,2,3 , \ldots \}{…,−3,−2,−1,0,1,2,3,…}

Write the set in set-builder notation. - {−3,−1,1,3,5,…}\{ - 3 , - 1,1,3,5 , \ldots \}{−3,−1,1,3,5,…}

Shade the regions representing the set. - (A∩B∩C′)′\left( A \cap B \cap C ^ { \prime } \right) ^ { \prime }(A∩B∩C′)′

Write the set in set-builder notation. -The set of all calculus books

The Art of Problem Solving

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

Find the number of proper subsets of the set. - $\{ x \mid x$ is a day of the week $\}$

Determine whether the statement is true or false. Let $A = \{ 1,3,5,7 \}$ B=\{5,6,7,8\} C=\{5,8\} D=\{2,5,8\} U=\{1,2,3,4,5,6,7,8\} - $C \subset D$

Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. $Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. Find n ( B \cup C )$ Find $n ( B \cup C )$

Decide whether the given statement is always true or not always true. - $( \mathrm { A } \cup \mathrm { B } ) ^ { \prime } = \mathrm { A } ^ { \prime } \cup \mathrm { B } ^ { \prime }$

List the elements in the set . Let =\{,,,,,,,,,\} =\{,,,,\} =\{,,,\} =\{,,,,\} - $\left( A \cup B ^ { \prime } \right) ^ { \prime } \cap C ^ { \prime }$

Find the indicated cardinal number. -Find $n ( A )$ given that $n ( A \times B ) = 36$ and $n ( B ) = 3$ .

Identify the set as finite or infinite. - $\{ x \mid x$ is a prime number $\}$

Write true or false for the following statement. Let A=\{3,5,7,9,11,13\} B=\{3,5,9,11\} C=\{5,9,13\} - $0 \in A$

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $9 \ldots \{ 4,5,6 , \ldots , 9 \}$

Shade the regions representing the set. - $A ^ { \prime } \cup B ^ { \prime }$ $Shade the regions representing the set. - A ^ { \prime } \cup B ^ { \prime }$

Tell whether the statement is true or false. - $\mathrm { k } \notin \{ p , a , k , h , v \}$

Write a description of the shaded region using the symbols A, B, C, $\cup$ , $\cap$ , -, and ' as needed. - $Write a description of the shaded region using the symbols A, B, C, \cup , \cap , -, and ' as needed. -$

Write the set in set-builder notation. - $\{ \ldots , - 3 , - 2 , - 1,0,1,2,3 , \ldots \}$

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

Shade the regions representing the set. - $\left( A \cap B \cap C ^ { \prime } \right) ^ { \prime }$ $Shade the regions representing the set. - \left( A \cap B \cap C ^ { \prime } \right) ^ { \prime }$