Question 1

Tell whether the statement is true or false.
-$\{ x \mid x \text { is a counting number greater than } 35 \} = \{ 35,36,37 , \ldots \}$

Accepted Answer

A) True 
 B)False

Question 2

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

Accepted Answer

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

Question 3

Decide whether $\subset$ ,$\subseteq$ , both, or neither can be placed in the blank to make a true statement.
-$\varnothing \ldots \{ 7,15,24,34 \}$

Accepted Answer

A)  Neither 
B)  $\subset$ 
C)  $\subseteq$ 
D)  Both$\subset$ and $\subseteq$ 
A)  Neither 
B)  $\subset$ 
C)  $\subseteq$ 
D)  Both$\subset$ and $\subseteq$

Question 4

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

Accepted Answer

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

Question 5

The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana. 
$\begin{array} { l l l } 
\underline { \text { Alabama } } & \underline { \text { Arkansas } } & \underline { \text { Louisiana } } \
\text { soybeans (s) } & \text { soybeans (s) } & \text { soybeans (s) } \
\text { peanuts (p) } & \text { rice (r) } & \text { sugarcane (n) } \
\text { corn (c) } & \text { cotton (t) } & \text { rice (r) } \
\text { hay (h) } & \text { hay (h) } & \text { corn (c) } \
\text { wheat (w) } & \text { wheat (w) } & \text { cotton (t) }
\end{array}$
 Let U be the smallest possible universal set that includes all of the crops listed, and let A, K and L be the sets of five crops in Alabama, Arkansas, and Louisiana, respectively. Find each of the following sets.
-$\mathrm { A } ^ { \prime } \cup \mathrm { L }$

Accepted Answer

A)  $\{ c , n , r , s , t \}$ 
B)  $\{ h , n , p , r , t , w \}$ 
C)  $\{ h , p , w \}$ 
D)  $\{ \mathrm { n } , \mathrm { r } , \mathrm { t } \}$ 
A)  $\{ c , n , r , s , t \}$ 
B)  $\{ h , n , p , r , t , w \}$ 
C)  $\{ h , p , w \}$ 
D)  $\{ \mathrm { n } , \mathrm { r } , \mathrm { t } \}$

Question 6

$\text { Use } \subset \text { or } \not \subset \text { in the blank to make a true statement. }$

-$\{ 3,5,7 \} \ldots \{ x \mid x$ is an odd counting number $\}$

Accepted Answer

A)  $\not \subset$ 
B)  $\subseteq$ 
A)  $\not \subset$ 
B)  $\subseteq$

Question 7

$\text { Use } \subset \text { or } \not \subset \text { in the blank to make a true statement. }$

-$\{ b , d , f , h \} \ldots \{ b , d , f , h , k \}$

Accepted Answer

A)  $\nsubseteq$ 
B)  $\subseteq$ 
A)  $\nsubseteq$ 
B)  $\subseteq$

Question 8

$\text { Use } \subset \text { or } \not \subset \text { in the blank to make a true statement. }$

-$\{ 12,39,44 \} \ldots \{ 9,39,44,54 \}$

Accepted Answer

A)  $\not \subset$ 
B)  $\subseteq$ 
A)  $\not \subset$ 
B)  $\subseteq$

Question 9

Decide whether the given statement is always true or not always true.
-If $\mathrm { B } \subseteq \mathrm { A }$, then $\mathrm { A } \cap \mathrm { B } = \mathrm { A }$

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

Write true or false for the following statement. Let
$\begin{array} { l } 
A = \{ 3,5,7,9,11,13 \} \
B = \{ 3,5,9,11 \} \
C = \{ 5,9,13 \}
\end{array}$
-$\{ x \mid x \text { is an odd counting number less than } 15 \} = A$

Accepted Answer

A) True 
 B)False

Question 13

$\text { Use } \subset \text { or } \not \subset \text { in the blank to make a true statement. }$

-$\varnothing \ldots \varnothing$

Accepted Answer

A)  $\not \subset$ 
B)  $\subseteq$ 
A)  $\not \subset$ 
B)  $\subseteq$

Question 14

A one-to-one correspondence between the set of counting numbers and the given set has been established. Find an expression for the nth term of the given set that corresponds to the counting number n.
-

Accepted Answer

A)  $- 11 \mathrm { n }$ 
B)  $n + 11$ 
C)  $11 \mathrm { n }$ 
D)  $\mathrm { n } - 11$ 
A)  $- 11 \mathrm { n }$ 
B)  $n + 11$ 
C)  $11 \mathrm { n }$ 
D)  $\mathrm { n } - 11$

Question 15

Let U = {all soda pops}, A = {all diet soda pops}, B = {all cola soda pops}, C = {all soda pops in cans}, and D = {all caffeine-free soda pops}. Describe the set in words.
-$A ^ { \prime } \cap C$

Accepted Answer

A)  All non-diet soda pops and all soda pops in cans 
B)  All diet soda pops and all soda pops in cans 
C)  All diet soda pops in cans 
D)  All non-diet soda pops in cans 
A)  All non-diet soda pops and all soda pops in cans 
B)  All diet soda pops and all soda pops in cans 
C)  All diet soda pops in cans 
D)  All non-diet soda pops in cans

Question 16

Determine whether the statement is true or false. 
Let $A = \{ 1,3,5,7 \}$
$\begin{array} { l } 
B = \{ 5,6,7,8 \} \
C = \{ 5,8 \} \
D = \{ 2,5,8 \} \
U = \{ 1,2,3,4,5,6,7,8 \}
\end{array}$
-$\{ 0 \} \subseteq \mathrm { U }$

Accepted Answer

A) True 
 B)False

Question 17

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.
-$\{ 7,12,17,22 , \ldots \}$

Accepted Answer

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

Question 18

The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana. 
$\begin{array} { l l l } 
\underline { \text { Alabama } } & \underline { \text { Arkansas } } & \underline { \text { Louisiana } } \
\hline \text { soybeans (s) } & \text { soybeans (s) } & \text { soybeans (s) } \
\text { peanuts (p) } & \text { rice (r) } & \text { sugarcane (n) } \
\text { corn (c) } & \text { cotton (t) } & \text { rice (r) } \
\text { hay (h) } & \text { hay (h) } & \text { corn (c) } \
\text { wheat (w) } & \text { wheat (w) } & \text { cotton (t) }
\end{array}$
 Let U be the smallest possible universal set that includes all of the crops listed, and let A, K and L be the sets of five crops
in Alabama, Arkansas, and Louisiana, respectively. Find each of the following sets.
-The set of crops in A'.

Accepted Answer

A) {n, r, t} 
B) {c, h, n, r, s, t, w} 
C) {h, n, r, t} 
D) {r, t} 
A) {n, r, t} 
B) {c, h, n, r, s, t, w} 
C) {h, n, r, t} 
D) {r, t}

Question 19

Let A and B be sets with cardinal numbers, n(A)= a and n(B)= b, respectively. Decide whether the statement is true or false.
-$\text { If } B \subseteq A , n ( B ) = n ( A ) - n ( A - B )$

Accepted Answer

A) True 
 B)False

Question 20

Find the cardinal number of the set.
-\{The set of points on a straight line\}

Accepted Answer

A)    
B)  $\mathrm { C }$ 
C)  1 
D)  0 
A)    
B)  $\mathrm { C }$ 
C)  1 
D)  0

Tell whether the statement is true or false. - $\{ x \mid x \text { is a counting number greater than } 35 \} = \{ 35,36,37 , \ldots \}$

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

Decide whether $\subset$ , $\subseteq$ , both, or neither can be placed in the blank to make a true statement. - $\varnothing \ldots \{ 7,15,24,34 \}$

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

$\text { Use } \subset \text { or } \not \subset \text { in the blank to make a true statement. }$ - $\{ 3,5,7 \} \ldots \{ x \mid x$ is an odd counting number $\}$

$\text { Use } \subset \text { or } \not \subset \text { in the blank to make a true statement. }$ - $\{ b , d , f , h \} \ldots \{ b , d , f , h , k \}$

$\text { Use } \subset \text { or } \not \subset \text { in the blank to make a true statement. }$ - $\{ 12,39,44 \} \ldots \{ 9,39,44,54 \}$

Decide whether the given statement is always true or not always true. -If $\mathrm { B } \subseteq \mathrm { A }$ , then $\mathrm { A } \cap \mathrm { B } = \mathrm { A }$

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 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 true or false for the following statement. Let A=\{3,5,7,9,11,13\} B=\{3,5,9,11\} C=\{5,9,13\} - $\{ x \mid x \text { is an odd counting number less than } 15 \} = A$

$\text { Use } \subset \text { or } \not \subset \text { in the blank to make a true statement. }$ - $\varnothing \ldots \varnothing$

A one-to-one correspondence between the set of counting numbers and the given set has been established. Find an expression for the nth term of the given set that corresponds to the counting number n. -

Let U = {all soda pops}, A = {all diet soda pops}, B = {all cola soda pops}, C = {all soda pops in cans}, and D = {all caffeine-free soda pops}. Describe the set in words. - $A ^ { \prime } \cap C$

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\} - $\{ 0 \} \subseteq \mathrm { U }$

Let A and B be sets with cardinal numbers, n(A)= a and n(B)= b, respectively. Decide whether the statement is true or false. - $\text { If } B \subseteq A , n ( B ) = n ( A ) - n ( A - B )$

Find the cardinal number of the set. -\{The set of points on a straight line\}

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

Tell whether the statement is true or false. - {x∣x is a counting number greater than 35}={35,36,37,…}\{ x \mid x \text { is a counting number greater than } 35 \} = \{ 35,36,37 , \ldots \}{x∣x is a counting number greater than 35}={35,36,37,…}

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

Decide whether ⊂\subset⊂ , ⊆\subseteq⊆ , both, or neither can be placed in the blank to make a true statement. - ∅…{7,15,24,34}\varnothing \ldots \{ 7,15,24,34 \}∅…{7,15,24,34}

Decide whether the given statement is always true or not always true. - A−A′=A\mathrm { A } - \mathrm { A } ^ { \prime } = \mathrm { A }A−A′=A

Decide whether the given statement is always true or not always true. -If B⊆A\mathrm { B } \subseteq \mathrm { A }B⊆A , then A∩B=A\mathrm { A } \cap \mathrm { B } = \mathrm { A }A∩B=A

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 true or false for the following statement. Let A=\{3,5,7,9,11,13\} B=\{3,5,9,11\} C=\{5,9,13\} - {x∣x is an odd counting number less than 15}=A\{ x \mid x \text { is an odd counting number less than } 15 \} = A{x∣x is an odd counting number less than 15}=A

Use ⊂ or ⊄ in the blank to make a true statement. \text { Use } \subset \text { or } \not \subset \text { in the blank to make a true statement. } Use ⊂ or ⊂ in the blank to make a true statement. - ∅…∅\varnothing \ldots \varnothing∅…∅

A one-to-one correspondence between the set of counting numbers and the given set has been established. Find an expression for the nth term of the given set that corresponds to the counting number n. -

Let U = {all soda pops}, A = {all diet soda pops}, B = {all cola soda pops}, C = {all soda pops in cans}, and D = {all caffeine-free soda pops}. Describe the set in words. - A′∩CA ^ { \prime } \cap CA′∩C

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\} - {0}⊆U\{ 0 \} \subseteq \mathrm { U }{0}⊆U

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. - {7,12,17,22,…}\{ 7,12,17,22 , \ldots \}{7,12,17,22,…}

Let A and B be sets with cardinal numbers, n(A)= a and n(B)= b, respectively. Decide whether the statement is true or false. - If B⊆A,n(B)=n(A)−n(A−B)\text { If } B \subseteq A , n ( B ) = n ( A ) - n ( A - B ) If B⊆A,n(B)=n(A)−n(A−B)

Find the cardinal number of the set. -\{The set of points on a straight line\}

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

Tell whether the statement is true or false. - $\{ x \mid x \text { is a counting number greater than } 35 \} = \{ 35,36,37 , \ldots \}$

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

Decide whether $\subset$ , $\subseteq$ , both, or neither can be placed in the blank to make a true statement. - $\varnothing \ldots \{ 7,15,24,34 \}$

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

Decide whether the given statement is always true or not always true. -If $\mathrm { B } \subseteq \mathrm { A }$ , then $\mathrm { A } \cap \mathrm { B } = \mathrm { A }$

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 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 true or false for the following statement. Let A=\{3,5,7,9,11,13\} B=\{3,5,9,11\} C=\{5,9,13\} - $\{ x \mid x \text { is an odd counting number less than } 15 \} = A$

$\text { Use } \subset \text { or } \not \subset \text { in the blank to make a true statement. }$ - $\varnothing \ldots \varnothing$

Let U = {all soda pops}, A = {all diet soda pops}, B = {all cola soda pops}, C = {all soda pops in cans}, and D = {all caffeine-free soda pops}. Describe the set in words. - $A ^ { \prime } \cap C$

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\} - $\{ 0 \} \subseteq \mathrm { U }$

Let A and B be sets with cardinal numbers, n(A)= a and n(B)= b, respectively. Decide whether the statement is true or false. - $\text { If } B \subseteq A , n ( B ) = n ( A ) - n ( A - B )$