Question 1

Decide whether $\subset$ ,$\subseteq$ , both, or neither can be placed in the blank to make a true statement.
-$\{ 5,6,7 \} \ldots \{ 5,6,7 \}$

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Determine whether or not the set is well defined.
-$\{ \mathrm { x } \mid \mathrm { x }$ is a adventure book in the library $\}$

Accepted Answer

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

Question 5

The lists below show five agricultural crops in Alabama, Arkansas, and Louisiana. 
$\begin{array} { l l l } 
\underline { \text { Alabama } } & \underline { \text { Arkansas } } & \underline { \text { Louisiana } } \
\hline \text { soybeans (s) } & \text { soybeans (s) } & \text { soybeans (s) } \
\text { peanuts (p) } & \text { rice (r) } & \text { sugarcane (n) } \
\text { corn (c) } & \text { cotton (t) } & \text { rice (r) } \
\text { hay (h) } & \text { hay (h) } & \text { corn (c) } \
\text { wheat (w) } & \text { wheat (w) } & \text { cotton (t) }
\end{array}$
 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) {c, n, p} 
B) {c,s} 
C) {h, n, p, r, t, w} 
D) {c, h, n, p, r, s, t, w} 
A) {c, n, p} 
B) {c,s} 
C) {h, n, p, r, t, w} 
D) {c, h, n, p, r, s, t, w}

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

A)  7 
B)  11 
C)  15 
D)  6 
A)  7 
B)  11 
C)  15 
D)  6

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

A) True 
 B)False

Question 11

Find the cardinal number of the set.
-$\{ x \mid x$ is a decimal between 63 and $64 \}$

Accepted Answer

A)   
B)  2 
C)    
D)  $\mathrm { c }$ 
A)   
B)  2 
C)    
D)  $\mathrm { c }$

Question 12

Find the indicated cardinal number.
-Find $n ( E )$, given that $n ( C \times E ) = 18$ and $C = \{ 4,5,6 \}$.

Accepted Answer

A)  54 
B)  9 
C)  6 
D)  3 
A)  54 
B)  9 
C)  6 
D)  3

Question 13

Determine whether the sets are equal, equivalent, both, or neither.
-{L, M, N, O} and {l, m, n, o}

Accepted Answer

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

Question 14

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets.
-{3, 4, 8, 9} and {-3, 4, -8, 9}

Accepted Answer

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

Question 15

Find the Cartesian product.
-$\begin{array} { l } 
A = \{ 5,15,2 \} \
B = \{ 6,10 \}
\end{array}$
Find $A \times B$.

Accepted Answer

A)  $\{ ( 5,6 ) , ( 15,10 ) \}$ 
B)  $\{ ( 5,6 ) , ( 5,10 ) , ( 15,6 ) , ( 15,10 ) , ( 2,6 ) , ( 2,10 ) \}$ 
C)  $\{ ( 6,5 ) , ( 6,15 ) , ( 6,2 ) , ( 10,5 ) , ( 10,15 ) , ( 10,2 ) \}$ 
D)  $\{ ( 5,6 ) , ( 15,2 ) , ( 2,6 ) \}$ 
A)  $\{ ( 5,6 ) , ( 15,10 ) \}$ 
B)  $\{ ( 5,6 ) , ( 5,10 ) , ( 15,6 ) , ( 15,10 ) , ( 2,6 ) , ( 2,10 ) \}$ 
C)  $\{ ( 6,5 ) , ( 6,15 ) , ( 6,2 ) , ( 10,5 ) , ( 10,15 ) , ( 10,2 ) \}$ 
D)  $\{ ( 5,6 ) , ( 15,2 ) , ( 2,6 ) \}$

Question 16

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

Accepted Answer

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

Decide whether $\subset$ , $\subseteq$ , both, or neither can be placed in the blank to make a true statement. - $\{ 5,6,7 \} \ldots \{ 5,6,7 \}$

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

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

Determine whether or not the set is well defined. - $\{ \mathrm { x } \mid \mathrm { x }$ is a adventure book in the library $\}$

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

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

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

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\} - $\{ 8,5,2 \} \subset \mathrm { D }$

Find the cardinal number of the set. - $\{ x \mid x$ is a decimal between 63 and $64 \}$

Find the indicated cardinal number. -Find $n ( E )$ , given that $n ( C \times E ) = 18$ and $C = \{ 4,5,6 \}$ .

Determine whether the sets are equal, equivalent, both, or neither. -{L, M, N, O} and {l, m, n, o}

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets. -{3, 4, 8, 9} and {-3, 4, -8, 9}

Find the Cartesian product. - A=\{5,15,2\} B=\{6,10\} Find $A \times B$ .

List the elements in the set . Let =\{,,,,,,,,,\} =\{,,,,\} =\{,,,\} =\{,,,,\} - $\mathrm { C } ^ { \prime } \cap \mathrm { A } ^ { \prime }$

The Art of Problem Solving

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Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

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Filters

Exam 2: The Basic Concepts of Set Theory

Decide whether ⊂\subset⊂ , ⊆\subseteq⊆ , both, or neither can be placed in the blank to make a true statement. - {5,6,7}…{5,6,7}\{ 5,6,7 \} \ldots \{ 5,6,7 \}{5,6,7}…{5,6,7}

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

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

Determine whether or not the set is well defined. - {x∣x\{ \mathrm { x } \mid \mathrm { x }{x∣x is a adventure book in the library }\}}

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

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

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

Decide whether the given statement is always true or not always true. - (A∪B)⊆A( \mathrm { A } \cup \mathrm { B } ) \subseteq \mathrm { A }(A∪B)⊆A

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\} - {8,5,2}⊂D\{ 8,5,2 \} \subset \mathrm { D }{8,5,2}⊂D

Find the cardinal number of the set. - {x∣x\{ x \mid x{x∣x is a decimal between 63 and 64}64 \}64}

Find the indicated cardinal number. -Find n(E)n ( E )n(E) , given that n(C×E)=18n ( C \times E ) = 18n(C×E)=18 and C={4,5,6}C = \{ 4,5,6 \}C={4,5,6} .