Question 1

Find n(A)for the set.
-$A = \{ x \mid x$ is a second in a minute $\}$

Accepted Answer

A)  $n ( A ) = 12$ 
B)  $n ( A ) = 60$ 
C)  $n ( A ) =$ Infinite 
D)  $n ( A ) = 120$ 
A)  $n ( A ) = 12$ 
B)  $n ( A ) = 60$ 
C)  $n ( A ) =$ Infinite 
D)  $n ( A ) = 120$ B

Question 2

Find n(A)for the set.
-$A = \{ 3,3,4,4 , \ldots , 7,7 \}$

Accepted Answer

A)  $n ( A ) = 6$ 
B)  $n ( A ) = 5$ 
C)  $n ( A ) = 3$ 
D)  $n ( A ) = 10$ 
A)  $n ( A ) = 6$ 
B)  $n ( A ) = 5$ 
C)  $n ( A ) = 3$ 
D)  $n ( A ) = 10$ B

Question 3

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

Accepted Answer

A) True 
 B)False  True

Question 4

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

Accepted Answer

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

Question 5

Tell whether the statement is true or false.
-(11, 7)= (7, 11)

Accepted Answer

A) True 
 B)False

Question 6

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 both A' and K'

Accepted Answer

A)  $\varnothing$ 
B)  $\{ n \}$ 
C)  $\{ c , p , r , t \}$ 
D)  $\{ c , n , p , r , t \}$ 
A)  $\varnothing$ 
B)  $\{ n \}$ 
C)  $\{ c , p , r , t \}$ 
D)  $\{ c , n , p , r , t \}$

Question 7

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets.
-{Mon, Tue, Wed} and {Oct, Nov, Dec}

Accepted Answer

A) Not possible 
B) Possible 
A) Not possible 
B) Possible

Question 8

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)  $3 \mathrm { n }$ 
B)  $3 n - 2$ 
C)  $3 n + 1$ 
D)  $3 n - 1$ 
A)  $3 \mathrm { n }$ 
B)  $3 n - 2$ 
C)  $3 n + 1$ 
D)  $3 n - 1$

Question 9

Tell whether the statement is true or false.
-{3, 6, 11} = {0, 3, 6, 11}

Accepted Answer

A) True 
 B)False

Question 10

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.
-$\mathrm { L } ^ { \prime } \cup \mathrm { K } ^ { \prime }$

Accepted Answer

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

Question 11

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets.
-{a, b, c, d} and {A, B, C, D}

Accepted Answer

A) Possible 
B) Not possible 
A) Possible 
B) Not possible

Question 12

Let U = {1, 2, 4, 5, a, b, c, d, e}. Find the complement of the set.
-R = {1, 2, 5, b, d}

Accepted Answer

A) {3, 4, a, b, c, e} 
B) {4, a, b, c, e} 
C) {4, a, c, e} 
D) {3, 4, a, c, e} 
A) {3, 4, a, b, c, e} 
B) {4, a, b, c, e} 
C) {4, a, c, e} 
D) {3, 4, a, c, e}

Question 13

Describe the conditions under which the statement is true.
-$A \cup B = A$

Accepted Answer

A)  $B \subseteq A$ 
B)  $B = \varnothing$ 
C)  $A \subseteq B$ 
D)  Always true 
A)  $B \subseteq A$ 
B)  $B = \varnothing$ 
C)  $A \subseteq B$ 
D)  Always true

Question 14

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

Accepted Answer

A)  All diet soda pops not in cans or all caffeine-free soda pops not in cans 
B)  All non-cola soda pops not in cans 
C)  All non-diet, non-caffeine-free soda pops not in cans 
D)  All diet, caffeine-free soda pops not in cans 
A)  All diet soda pops not in cans or all caffeine-free soda pops not in cans 
B)  All non-cola soda pops not in cans 
C)  All non-diet, non-caffeine-free soda pops not in cans 
D)  All diet, caffeine-free soda pops not in cans

Question 15

Decide whether $\subset$ ,$\subseteq$ , both, or neither can be placed in the blank to make a true statement.
-$\{ a , b \} \ldots \{ z , a , y , b , x , c \}$

Accepted Answer

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

Question 16

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

Accepted Answer

A) True 
 B)False

Question 17

Write the set in set-builder notation.
-$\{ 2,4,6,8 \}$

Accepted Answer

A)  $\{ 2,4,6,8 \}$ 
B)  $\{ x \mid x$ is an even natural number less than $10 \}$ 
C)  $\{ x \mid x$ is any even integer less than $10 \}$ 
D)  $\{ x \mid x$ is any even natural number $\}$ 
A)  $\{ 2,4,6,8 \}$ 
B)  $\{ x \mid x$ is an even natural number less than $10 \}$ 
C)  $\{ x \mid x$ is any even integer less than $10 \}$ 
D)  $\{ x \mid x$ is any even natural number $\}$

Question 18

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.
-$\{ 1,8,27,64 , \ldots \}$

Accepted Answer

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

Question 19

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets.
-{0} and {856}

Accepted Answer

A) Possible 
B) Not possible 
A) Possible 
B) Not possible

Question 20

Find the number of proper subsets of the set.
-{1, 2, 3, ..., 8}

Accepted Answer

A) 250 
B) 511 
C) 256 
D) 255 
A) 250 
B) 511 
C) 256 
D) 255

Find n(A)for the set. - $A = \{ x \mid x$ is a second in a minute $\}$

Find n(A)for the set. - $A = \{ 3,3,4,4 , \ldots , 7,7 \}$

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\} - $9 \in B$

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

Tell whether the statement is true or false. -(11, 7)= (7, 11)

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets. -{Mon, Tue, Wed} and {Oct, Nov, Dec}

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. -

Tell whether the statement is true or false. -{3, 6, 11} = {0, 3, 6, 11}

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets. -{a, b, c, d} and {A, B, C, D}

Let U = {1, 2, 4, 5, a, b, c, d, e}. Find the complement of the set. -R = {1, 2, 5, b, d}

Describe the conditions under which the statement is true. - $A \cup B = A$

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

Decide whether $\subset$ , $\subseteq$ , both, or neither can be placed in the blank to make a true statement. - $\{ a , b \} \ldots \{ z , a , y , b , x , c \}$

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\} - $\phi \subseteq \mathrm { A }$

Write the set in set-builder notation. - $\{ 2,4,6,8 \}$

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets. -{0} and {856}

Find the number of proper subsets of the set. -{1, 2, 3, ..., 8}

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 n(A)for the set. - A={x∣xA = \{ x \mid xA={x∣x is a second in a minute }\}}

Find n(A)for the set. - A={3,3,4,4,…,7,7}A = \{ 3,3,4,4 , \ldots , 7,7 \}A={3,3,4,4,…,7,7}

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\} - 9∈B9 \in B9∈B

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

Tell whether the statement is true or false. -(11, 7)= (7, 11)

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets. -{Mon, Tue, Wed} and {Oct, Nov, Dec}

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. -

Tell whether the statement is true or false. -{3, 6, 11} = {0, 3, 6, 11}

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets. -{a, b, c, d} and {A, B, C, D}

Let U = {1, 2, 4, 5, a, b, c, d, e}. Find the complement of the set. -R = {1, 2, 5, b, d}

Describe the conditions under which the statement is true. - A∪B=AA \cup B = AA∪B=A

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∪D)∩C′( \mathrm { A } \cup \mathrm { D } ) \cap \mathrm { C } ^ { \prime }(A∪D)∩C′

Decide whether ⊂\subset⊂ , ⊆\subseteq⊆ , both, or neither can be placed in the blank to make a true statement. - {a,b}…{z,a,y,b,x,c}\{ a , b \} \ldots \{ z , a , y , b , x , c \}{a,b}…{z,a,y,b,x,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\} - ϕ⊆A\phi \subseteq \mathrm { A }ϕ⊆A

Write the set in set-builder notation. - {2,4,6,8}\{ 2,4,6,8 \}{2,4,6,8}

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. - {1,8,27,64,…}\{ 1,8,27,64 , \ldots \}{1,8,27,64,…}

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets. -{0} and {856}

Find the number of proper subsets of the set. -{1, 2, 3, ..., 8}

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 n(A)for the set. - $A = \{ x \mid x$ is a second in a minute $\}$

Find n(A)for the set. - $A = \{ 3,3,4,4 , \ldots , 7,7 \}$

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\} - $9 \in B$

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

Describe the conditions under which the statement is true. - $A \cup B = A$

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

Decide whether $\subset$ , $\subseteq$ , both, or neither can be placed in the blank to make a true statement. - $\{ a , b \} \ldots \{ z , a , y , b , x , c \}$

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\} - $\phi \subseteq \mathrm { A }$

Write the set in set-builder notation. - $\{ 2,4,6,8 \}$