Question 1

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

Accepted Answer

A) {c, 3} 
B) $ \varnothing$ 
C) {c} 
D) U 
A) {c, 3} 
B) $ \varnothing$ 
C) {c} 
D) U

Question 2

For the given sets, construct a Venn diagram and place the elements in the proper region.
-$\begin{array}{l}
\text { Let } U=\{b, d, j, i, m, n, t\} \
A=\{d, j, i, n\} \
B=\{b, d, j, t\}
\end{array}$

Accepted Answer

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

Question 3

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 either A' or L or both

Accepted Answer

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

Question 4

Find the indicated cardinal number.
-Find $n ( A \times B )$ given that $n ( A ) = 34$ and $n ( B ) = 10$.

Accepted Answer

A)  54 
B)  340 
C)  44 
D)  24 
A)  54 
B)  340 
C)  44 
D)  24

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.
-$A \cup L$

Accepted Answer

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

Question 6

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets.
-{1, 2, 3, 4, ...} and {0, 1, 2, 3, 4}

Accepted Answer

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

Question 7

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

-$\{ 4,6,8 \} ... \{ 3,4,5,6,8 \}$

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Tell whether the statement is true or false.
-$\{ 2,17,28,7,36 \} = \{ 36,17,7,82,2 \}$

Accepted Answer

A) True 
 B)False

Question 10

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

Accepted Answer

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

Question 11

For the given sets, construct a Venn diagram and place the elements in the proper region.
-$\begin{array} { l } 
\mathrm { U } = \{ 2,4,6,8,10,12 \} \
\mathrm { A } = \{ 2,6,10 \} \
\mathrm { B } = \{ 2,4,8 \} \
\mathrm { C } = \{ 2,8,10,12 \}
\end{array}$

Accepted Answer

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

Question 12

Determine whether the sets are equal, equivalent, both, or neither.
-$\{ x \mid x$ is a whole number $\}$ and $\{ x \mid x$ is an integer $\}$

Accepted Answer

A)  Equivalent 
B)  Both 
C)  Equal 
D)  Neither 
A)  Equivalent 
B)  Both 
C)  Equal 
D)  Neither

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)  $- 200 n$ 
B)  $\mathrm { n } - 200$ 
C)  $\mathrm { n } + 200$ 
D)  $200 \mathrm { n }$ 
A)  $- 200 n$ 
B)  $\mathrm { n } - 200$ 
C)  $\mathrm { n } + 200$ 
D)  $200 \mathrm { n }$

Question 14

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

Accepted Answer

A) True 
 B)False

Question 15

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

Accepted Answer

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

Question 16

Find the Cartesian product.
-$A = \{ 0 \}$
 $B = \{ 20,30,40 \}$
 Find $B \times A .$

Accepted Answer

A)  $\{ 0,0,0 \}$ 
B)  $\{ ( 20,0 ) , ( 30,0 ) , ( 40,0 ) \}$ 
C)  $\{ ( 0,20 ) , ( 0,30 ) , ( 0,40 ) \}$ 
D)  $\{ 0 \}$ 
A)  $\{ 0,0,0 \}$ 
B)  $\{ ( 20,0 ) , ( 30,0 ) , ( 40,0 ) \}$ 
C)  $\{ ( 0,20 ) , ( 0,30 ) , ( 0,40 ) \}$ 
D)  $\{ 0 \}$

Question 17

Find the cardinal number of the set.
-The numbers in the Venn Diagram below represent cardinalities.  
Find $n \left( A \cap B ^ { \prime } \right)$.

Accepted Answer

A)  24 
B)  28 
C)  4 
D)  20 
A)  24 
B)  28 
C)  4 
D)  20

Question 18

Solve the problem.
-A survey of 134 college students was done to find out what elective courses they were taking. Let A = the set of those taking art, $B =$ the set of those taking basketweaving, and $C =$ the set of those taking canoeing. The study revealed the following information.
$\begin{array} { l l } 
n ( A ) = 45 & n ( A \cap B ) = 12 \
n ( B ) = 55 & n ( A \cap C ) = 15 \
n ( C ) = 40 & n ( B \cap C ) = 23 \
n ( A \cap B \cap C ) = 2
\end{array}$
 How many students were not taking any of these electives?

Accepted Answer

A) 52 
B) 10 
C) 44 
D) 42 
A) 52 
B) 10 
C) 44 
D) 42

Question 19

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

Accepted Answer

A) True 
 B)False

Question 20

Find the indicated cardinal number.
-Find $n ( A \times B )$ given that $A = \{ 2 \}$ and $B = \{ 1,3 \}$.

Accepted Answer

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

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

Find the indicated cardinal number. -Find $n ( A \times B )$ given that $n ( A ) = 34$ and $n ( B ) = 10$ .

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets. -{1, 2, 3, 4, ...} and {0, 1, 2, 3, 4}

$\text { Use } \subset \text { or } \not \subset \text { in the blank to make a true statement. }$ - $\{ 4,6,8 \} ... \{ 3,4,5,6,8 \}$

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

Tell whether the statement is true or false. - $\{ 2,17,28,7,36 \} = \{ 36,17,7,82,2 \}$

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

Determine whether the sets are equal, equivalent, both, or neither. - $\{ x \mid x$ is a whole number $\}$ and $\{ x \mid x$ is an integer $\}$

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. -

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\} - $\{ 13 \} \in B$

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

Find the Cartesian product. - $A = \{ 0 \}$ $B = \{ 20,30,40 \}$ Find $B \times A .$

Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. $Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. Find n \left( A \cap B ^ { \prime } \right) .$ Find $n \left( A \cap B ^ { \prime } \right)$ .

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\} - $\{ 6,5,8,7 \} \subseteq \mathrm { B }$

Find the indicated cardinal number. -Find $n ( A \times B )$ given that $A = \{ 2 \}$ and $B = \{ 1,3 \}$ .

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

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

For the given sets, construct a Venn diagram and place the elements in the proper region. - Let U=\{b,d,j,i,m,n,t\} A=\{d,j,i,n\} B=\{b,d,j,t\}

Find the indicated cardinal number. -Find n(A×B)n ( A \times B )n(A×B) given that n(A)=34n ( A ) = 34n(A)=34 and n(B)=10n ( B ) = 10n(B)=10 .

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets. -{1, 2, 3, 4, ...} and {0, 1, 2, 3, 4}

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. - {4,6,8}...{3,4,5,6,8}\{ 4,6,8 \} ... \{ 3,4,5,6,8 \}{4,6,8}...{3,4,5,6,8}

Decide whether the given statement is always true or not always true. - A∩(B∪C)=(A∩B)∪CA \cap ( B \cup C ) = ( A \cap B ) \cup CA∩(B∪C)=(A∩B)∪C

Tell whether the statement is true or false. - {2,17,28,7,36}={36,17,7,82,2}\{ 2,17,28,7,36 \} = \{ 36,17,7,82,2 \}{2,17,28,7,36}={36,17,7,82,2}

List the elements in the set . Let =\{,,,,,,,,,\} =\{,,,,\} =\{,,,\} =\{,,,,\} - A∪(B∩C)\mathrm { A } \cup ( \mathrm { B } \cap \mathrm { C } )A∪(B∩C)

For the given sets, construct a Venn diagram and place the elements in the proper region. - =\{2,4,6,8,10,12\} =\{2,6,10\} =\{2,4,8\} =\{2,8,10,12\}

Determine whether the sets are equal, equivalent, both, or neither. - {x∣x\{ x \mid x{x∣x is a whole number }\}} and {x∣x\{ x \mid x{x∣x is an integer }\}}

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. -

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\} - {13}∈B\{ 13 \} \in B{13}∈B

Shade the regions representing the set. - A′∩B′\mathrm { A } ^ { \prime } \cap \mathrm { B } ^ { \prime }A′∩B′

Find the Cartesian product. - A={0}A = \{ 0 \}A={0} B={20,30,40}B = \{ 20,30,40 \}B={20,30,40} Find B×A.B \times A .B×A.

Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. Find n(A∩B′)n \left( A \cap B ^ { \prime } \right)n(A∩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\} - {6,5,8,7}⊆B\{ 6,5,8,7 \} \subseteq \mathrm { B }{6,5,8,7}⊆B

Find the indicated cardinal number. -Find n(A×B)n ( A \times B )n(A×B) given that A={2}A = \{ 2 \}A={2} and B={1,3}B = \{ 1,3 \}B={1,3} .

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 indicated cardinal number. -Find $n ( A \times B )$ given that $n ( A ) = 34$ and $n ( B ) = 10$ .

$\text { Use } \subset \text { or } \not \subset \text { in the blank to make a true statement. }$ - $\{ 4,6,8 \} ... \{ 3,4,5,6,8 \}$

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

Tell whether the statement is true or false. - $\{ 2,17,28,7,36 \} = \{ 36,17,7,82,2 \}$

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

Determine whether the sets are equal, equivalent, both, or neither. - $\{ x \mid x$ is a whole number $\}$ and $\{ x \mid x$ is an integer $\}$

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\} - $\{ 13 \} \in B$

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

Find the Cartesian product. - $A = \{ 0 \}$ $B = \{ 20,30,40 \}$ Find $B \times A .$

Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. $Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. Find n \left( A \cap B ^ { \prime } \right) .$ Find $n \left( A \cap B ^ { \prime } \right)$ .

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\} - $\{ 6,5,8,7 \} \subseteq \mathrm { B }$

Find the indicated cardinal number. -Find $n ( A \times B )$ given that $A = \{ 2 \}$ and $B = \{ 1,3 \}$ .