Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

A) True 
 B)False

Question 3

Find the indicated cardinal number.
-Find $n ( F )$, given that $n ( B \times F ) = 18$ and $B = \{ 1,3 \}$.

Accepted Answer

A)  6 
B)  54 
C)  9 
D)  36 
A)  6 
B)  54 
C)  9 
D)  36

Question 4

For the given sets, construct a Venn diagram and place the elements in the proper region.
-$\begin{array} { l } 
\mathrm { U } = \{ \mathrm { a } , \mathrm { b } , \mathrm { c } , \mathrm { d } , \mathrm { e } , \mathrm { f } , \mathrm { g } , \mathrm { h } , \mathrm { i } , \mathrm { j } , \mathrm { k } , \mathrm { l } , \mathrm { m } , \mathrm { n } , \mathrm { o } , \mathrm { p } \} \
\mathrm { A } = \{ \mathrm { a } , \mathrm { e } , \mathrm { i } , \mathrm { o } \} \
\mathrm { B } = \{ \mathrm { b } , \mathrm { c } , \mathrm { d } , \mathrm { f } , \mathrm { g } , \mathrm { h } , \mathrm { j } , \mathrm { k } , \mathrm { l } , \mathrm { m } \} \
\mathrm { C } = \{ \mathrm { a } , \mathrm { b } , \mathrm { c } , \mathrm { d } , \mathrm { e } , \mathrm { f } , \mathrm { g } \}
\end{array}$

Accepted Answer

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

Question 5

Decide whether the given statement is always true or not always true.
-$( A \cap B ) \subseteq B$

Accepted Answer

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

Question 6

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)  $1000 ^ { \mathrm { n } }$ 
B)  $n 1000$ 
C)  $- 1000 n$ 
D)  $1000 \mathrm { n }$ 
A)  $1000 ^ { \mathrm { n } }$ 
B)  $n 1000$ 
C)  $- 1000 n$ 
D)  $1000 \mathrm { n }$

Question 7

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

Accepted Answer

A) {1, 5, a, e} 
B) {1, 2, 4, 5, a, b, c, d, e} 
C) {1, 5, a, c, e} 
D) {1, 3, 5, a, c, e} 
A) {1, 5, a, e} 
B) {1, 2, 4, 5, a, b, c, d, e} 
C) {1, 5, a, c, e} 
D) {1, 3, 5, a, c, e}

Question 8

Find the number of proper subsets of the set.
-$\{ x \mid x$ is an even number between 19 and $33 \}$

Accepted Answer

A)  128 
B)  64 
C)  127 
D)  32 
A)  128 
B)  64 
C)  127 
D)  32

Question 9

Solve the problem.
-List all possible proper subsets of the set {2, 6, 7}.

Accepted Answer

A)  $\{ 2 \} , \{ 6 \} , \{ 7 \} , \{ 2,6 \} , \{ 2,7 \} , \{ 6,7 \} , \{ 2,6,7 \}$ 
B)  $\varnothing , \{ 2 \} , \{ 6 \} , \{ 7 \} , \{ 2,6 \} , \{ 2,7 \} , \{ 6,7 \} , \{ 2,6,7 \}$ 
C)  $\varnothing , \{ 2 \} , \{ 6 \} , \{ 7 \} , \{ 2,6 \} , \{ 2,7 \} , \{ 6,7 \}$ 
D)  $\{ 2 \} , \{ 6 \} , \{ 7 \} , \{ 2,6 \} , \{ 2,7 \} , \{ 6,7 \}$ 
A)  $\{ 2 \} , \{ 6 \} , \{ 7 \} , \{ 2,6 \} , \{ 2,7 \} , \{ 6,7 \} , \{ 2,6,7 \}$ 
B)  $\varnothing , \{ 2 \} , \{ 6 \} , \{ 7 \} , \{ 2,6 \} , \{ 2,7 \} , \{ 6,7 \} , \{ 2,6,7 \}$ 
C)  $\varnothing , \{ 2 \} , \{ 6 \} , \{ 7 \} , \{ 2,6 \} , \{ 2,7 \} , \{ 6,7 \}$ 
D)  $\{ 2 \} , \{ 6 \} , \{ 7 \} , \{ 2,6 \} , \{ 2,7 \} , \{ 6,7 \}$

Question 10

Determine whether or not the set is well defined.
-\{x| $x$ is an expensive boat on the Great Lakes $\}$

Accepted Answer

A)  Well defined 
B)  Not well defined 
A)  Well defined 
B)  Not well defined

Question 11

Describe the conditions under which the statement is true.
-$A \cap B ^ { \prime } = A$

Accepted Answer

A)  $A \cap B = \varnothing$ 
B)  $\mathrm { B } \subseteq \mathrm { A }$ 
C)  Always true 
D)  $B = \varnothing$ 
A)  $A \cap B = \varnothing$ 
B)  $\mathrm { B } \subseteq \mathrm { A }$ 
C)  Always true 
D)  $B = \varnothing$

Question 12

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.
-$n ( A \cap B ) = n ( B \cap A )$

Accepted Answer

A) True 
 B)False

Question 13

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)  $5 n + 2$ 
B)  $- 5 n + 2$ 
C)  $- 5 n - 2$ 
D)  $5 n - 2$ 
A)  $5 n + 2$ 
B)  $- 5 n + 2$ 
C)  $- 5 n - 2$ 
D)  $5 n - 2$

Question 14

Solve the problem.
-Monticello residents were surveyed concerning their preferences for candidates Moore and Allen in an upcoming election. Of the 800 respondents, 300 support neither Moore nor Allen, 100 support Both Moore and Allen, and 250 support only Moore. How many residents support Moore or Allen?

Accepted Answer

A) 400 
B) 300 
C) 100 
D) 500 
A) 400 
B) 300 
C) 100 
D) 500

Question 15

Find the number of subsets of the set.
-{mom, dad, son, daughter}

Accepted Answer

A) 8 
B) 12 
C) 16 
D) 14 
A) 8 
B) 12 
C) 16 
D) 14

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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)  $2 n - 1$ 
B)  $2 n + 1$ 
C)  $2 n$ 
D)  $2 ^ { n }$ 
A)  $2 n - 1$ 
B)  $2 n + 1$ 
C)  $2 n$ 
D)  $2 ^ { n }$

Question 19

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

Accepted Answer

A) {1, 2, 3, 4, 5, e} 
B) {e} 
C) {1, 2, 4, 5} 
D) {1, 2, 4, 5, e} 
A) {1, 2, 3, 4, 5, e} 
B) {e} 
C) {1, 2, 4, 5} 
D) {1, 2, 4, 5, e}

Question 20

Find the indicated cardinal number.
-Find $n ( A \times C )$ given that $A = \{ 2 \}$ and $C = \{ 4,5,6 \}$.

Accepted Answer

A)  4 
B)  3 
C)  2 
D)  1 
A)  4 
B)  3 
C)  2 
D)  1

List the elements in the set . Let =\{,,,,,,,,,\} =\{,,,,\} =\{,,,\} =\{,,,,\} - $A ^ { \prime } \cup B$

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\} - $C \nsubseteq B$

Find the indicated cardinal number. -Find $n ( F )$ , given that $n ( B \times F ) = 18$ and $B = \{ 1,3 \}$ .

Decide whether the given statement is always true or not always true. - $( A \cap B ) \subseteq B$

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

Find the number of proper subsets of the set. - $\{ x \mid x$ is an even number between 19 and $33 \}$

Solve the problem. -List all possible proper subsets of the set {2, 6, 7}.

Determine whether or not the set is well defined. -\{x| $x$ is an expensive boat on the Great Lakes $\}$

Describe the conditions under which the statement is true. - $A \cap B ^ { \prime } = A$

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. - $n ( A \cap B ) = n ( B \cap A )$

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. -

Find the number of subsets of the set. -{mom, dad, son, daughter}

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

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

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

Find the indicated cardinal number. -Find $n ( A \times C )$ given that $A = \{ 2 \}$ and $C = \{ 4,5,6 \}$ .

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

List the elements in the set . Let =\{,,,,,,,,,\} =\{,,,,\} =\{,,,\} =\{,,,,\} - A′∪BA ^ { \prime } \cup BA′∪B

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⊈BC \nsubseteq BC⊈B

Find the indicated cardinal number. -Find n(F)n ( F )n(F) , given that n(B×F)=18n ( B \times F ) = 18n(B×F)=18 and B={1,3}B = \{ 1,3 \}B={1,3} .

For the given sets, construct a Venn diagram and place the elements in the proper region. - =\{,,,,,,,,,,,,,,,\} =\{,,,\} =\{,,,,,,,,,\} =\{,,,,,,\}

Decide whether the given statement is always true or not always true. - (A∩B)⊆B( A \cap B ) \subseteq B(A∩B)⊆B

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

Find the number of proper subsets of the set. - {x∣x\{ x \mid x{x∣x is an even number between 19 and 33}33 \}33}

Solve the problem. -List all possible proper subsets of the set {2, 6, 7}.

Determine whether or not the set is well defined. -\{x| xxx is an expensive boat on the Great Lakes }\}}

Describe the conditions under which the statement is true. - A∩B′=AA \cap B ^ { \prime } = AA∩B′=A

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. - n(A∩B)=n(B∩A)n ( A \cap B ) = n ( B \cap A )n(A∩B)=n(B∩A)

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. -

Find the number of subsets of the set. -{mom, dad, son, daughter}

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

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

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

Find the indicated cardinal number. -Find n(A×C)n ( A \times C )n(A×C) given that A={2}A = \{ 2 \}A={2} and C={4,5,6}C = \{ 4,5,6 \}C={4,5,6} .

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

List the elements in the set . Let =\{,,,,,,,,,\} =\{,,,,\} =\{,,,\} =\{,,,,\} - $A ^ { \prime } \cup B$

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\} - $C \nsubseteq B$

Find the indicated cardinal number. -Find $n ( F )$ , given that $n ( B \times F ) = 18$ and $B = \{ 1,3 \}$ .

Decide whether the given statement is always true or not always true. - $( A \cap B ) \subseteq B$

Find the number of proper subsets of the set. - $\{ x \mid x$ is an even number between 19 and $33 \}$

Determine whether or not the set is well defined. -\{x| $x$ is an expensive boat on the Great Lakes $\}$

Describe the conditions under which the statement is true. - $A \cap B ^ { \prime } = A$

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. - $n ( A \cap B ) = n ( B \cap A )$

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

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

Find the indicated cardinal number. -Find $n ( A \times C )$ given that $A = \{ 2 \}$ and $C = \{ 4,5,6 \}$ .