Question 1

Tell whether the statement is true or false. If false, give the reason.
-{54, 55, 54, 55} = {54, 55}

Accepted Answer

A)  False; the elements cannot be repeated. 
B)  False; the elements are not equal. 
C)  True 
D)  False; there must be the same number of elements. 
A)  False; the elements cannot be repeated. 
B)  False; the elements are not equal. 
C)  True 
D)  False; there must be the same number of elements.

Question 2

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}.
Determine whether the statement is true or false.
-D ⊄ D

Accepted Answer

A)  True 
B)  False; A is a subset of itself. 
C)  False; A is not a subset of itself. 
D)  False; the set is equal to itself. 
A)  True 
B)  False; A is a subset of itself. 
C)  False; A is not a subset of itself. 
D)  False; the set is equal to itself.

Question 3

Solve the problem.
-Use the following graph which shows the number of customer service calls to a major appliance Manufacturer, in millions, for the years 2006-2012. Use the graph to represent the set in roster Form.  
The set of years in which the number of customer service calls exceeded 1.1 million.

Accepted Answer

A)  {2009, 2012} 
B)  {2006, 2007, 2008, 2010, 2011} 
C)  {2006, 2007, 2008, 2009, 2010, 2011} 
D)  {2006, 2007, 2008, 2011} 
A)  {2009, 2012} 
B)  {2006, 2007, 2008, 2010, 2011} 
C)  {2006, 2007, 2008, 2009, 2010, 2011} 
D)  {2006, 2007, 2008, 2011}

Question 4

Determine whether the set is well defined or not well defined.
-The set of rivers that flow south to north

Accepted Answer

A)  not well defined 
B)  well defined 
A)  not well defined 
B)  well defined

Question 5

Determine whether the set is well defined or not well defined.
-The set of children in fifth grade at Maple Elementary School that are girls

Accepted Answer

A)  not well defined 
B)  well defined 
A)  not well defined 
B)  well defined

Question 6

Tell whether the statement is true or false. If false, give the reason.
-15 ∉ {x|x is an even counting number}

Accepted Answer

A)  False; 15 is a counting number. 
B)  False; 15 is an even counting number. 
C)  False; 15 is an element of the set. 
D)  True 
A)  False; 15 is a counting number. 
B)  False; 15 is an even counting number. 
C)  False; 15 is an element of the set. 
D)  True

Question 7

Find n(A) for the set.
-A = {800, 801, 802, . . ., 8000}

Accepted Answer

A)  n(
A)  = 7200 
B)  n(
A)  = 7201 
C)  n(
A)  = 8000 
D)  n(
A)  = 4 
A)  n(
A)  = 7200 
B)  n(
A)  = 7201 
C)  n(
A)  = 8000 
D)  n(
A)  = 4

Question 8

Express the set in roster form.
-{x|x is a natural number multiple of 5}

Accepted Answer

A)  {0, 5, 10, 15,. . .} 
B)  {5, 10, 15, . . .} 
C)  {10, 15, 20, . . .} 
D)  ∅ 
A)  {0, 5, 10, 15,. . .} 
B)  {5, 10, 15, . . .} 
C)  {10, 15, 20, . . .} 
D)  ∅

Question 9

Use $ \subseteq, \nsubseteq, \subset $, or both $ \subset $ and $ \subseteq$ to make a true statement.
-$\{ \mathrm { s } , \mathrm { r } , \mathrm { t } \} ........  \{ \mathrm { s } , \mathrm { r } , \mathrm { t } \}$

Accepted Answer

A)  $ \subseteq $ and $\subset $ 
B)  $\subset$ 
C)  $\nsubseteq$ 
D)  $\subseteq$ 
A)  $ \subseteq $ and $\subset $ 
B)  $\subset$ 
C)  $\nsubseteq$ 
D)  $\subseteq$

Question 10

Express the set in roster form.
-The set of the days of the week

Accepted Answer

A)  {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday} 
B)  {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} 
C)  {Saturday, Sunday} 
D)  {Tuesday, Thursday} 
A)  {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday} 
B)  {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Sunday} 
C)  {Saturday, Sunday} 
D)  {Tuesday, Thursday}

Question 11

If the statement is true for all sets C and D, write ʺtrue.ʺ If it is not true for all sets C and D, write ʺfalse.ʺ Assume that $ C \not = \varnothing $,and $ C \subset U$.
-$ \varnothing \subset \varnothing $

Accepted Answer

A) True 
 B)False

Question 12

Use $ \subseteq, \nsubseteq, \subset $, or both $ \subset $ and $ \subseteq$ to make a true statement.
-$\{ 6,7,8 \}$ ____$\{ 6,7,8 \}$

Accepted Answer

A)  $\subseteq$ 
B)  $\subset$
 and$\nsubseteq$ 
C)  $\subset$ 
D)  $\nsubseteq$ 
A)  $\subseteq$ 
B)  $\subset$
 and$\nsubseteq$ 
C)  $\subset$ 
D)  $\nsubseteq$

Question 13

Solve the problem.
-Use the following graph, which shows the sales of digital music players, in millions, at a national Electronics retail store for the years 2005-2012. Use the graph to represent the set in roster form.  
The set of years included in the graph in which digital music player sales were more than 18 Million.

Accepted Answer

A)  {2005, 2006, 2007, 2008, 2009, 2010, 2011} 
B)  {0} 
C)  { } 
D)  {2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012} 
A)  {2005, 2006, 2007, 2008, 2009, 2010, 2011} 
B)  {0} 
C)  { } 
D)  {2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012}

Question 14

Write a description of the set.
-E = {x | x ∈ N and 2 < x ≤ 19}

Accepted Answer

A)  E is the set of integers greater than 2 and less than or equal to 19. 
B)  E is the set of natural numbers greater than or equal to 2 and less than 19. 
C)  E is the set of natural numbers greater than 19 and less than or equal to 2. 
D)  E is the set of natural numbers greater than 2 and less than or equal to 19. 
A)  E is the set of integers greater than 2 and less than or equal to 19. 
B)  E is the set of natural numbers greater than or equal to 2 and less than 19. 
C)  E is the set of natural numbers greater than 19 and less than or equal to 2. 
D)  E is the set of natural numbers greater than 2 and less than or equal to 19.

Question 15

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 integer $\}$ 
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 integer $\}$ 
D)  $\{ x \mid x$ is any even natural number $\}$

Question 16

Determine whether the set is well defined or not well defined.
-The set of people who wear expensive clothes

Accepted Answer

A)  not well defined 
B)  well defined 
A)  not well defined 
B)  well defined

Question 17

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

Accepted Answer

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

Question 18

Express the set in roster form.
-The set of all whole numbers greater than 2 and less than 6

Accepted Answer

A)  {2, 3, 4, 5} 
B)  {2, 3, 4, 5, 6} 
C)  {3, 4, 5, 6} 
D)  {3, 4, 5} 
A)  {2, 3, 4, 5} 
B)  {2, 3, 4, 5, 6} 
C)  {3, 4, 5, 6} 
D)  {3, 4, 5}

Question 19

Express the set in roster form.
-The set of seasons in a year

Accepted Answer

A)  {winter, spring, summer, fall} 
B)  {January, March, June, September} 
C)  {cold, warm, hot, cool} 
D)  {winter, summer} 
A)  {winter, spring, summer, fall} 
B)  {January, March, June, September} 
C)  {cold, warm, hot, cool} 
D)  {winter, summer}

Question 20

Solve the problem.
-Use the following table, which shows the average price for a new beverage that is served at a Coffee chain. Let the 10 selected regions represent the universal set. Use the list to represent the set In roster form. $$\begin{array} { c | r } 
\text { Region } & \text { Price } \
\hline \mathrm { A } & \$ 7.58 \
\mathrm {~B} & \$ 6.67 \
\mathrm { C } & \$ 6.45 \
\mathrm { D } & \$ 5.86 \
\mathrm { E } & \$ 4.59 \
\mathrm {~F} & \$ 3.67 \
\mathrm { G } & \$ 3.47 \
\mathrm { H } & \$ 2.99 \
\mathrm {~K} & \$ 2.33 \
\mathrm {~L} & \$ 1.77
\end{array}$$
The set of regions in which the average price for the new beverage is more than $5.00.

Accepted Answer

A)  {A, B, C, D} 
B)  {A, B, C} 
C)  {E, F, G, H, K, L} 
D)  {A, B, C, D, E} 
A)  {A, B, C, D} 
B)  {A, B, C} 
C)  {E, F, G, H, K, L} 
D)  {A, B, C, D, E}

Tell whether the statement is true or false. If false, give the reason. -{54, 55, 54, 55} = {54, 55}

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}. Determine whether the statement is true or false. -D ⊄ D

Determine whether the set is well defined or not well defined. -The set of rivers that flow south to north

Determine whether the set is well defined or not well defined. -The set of children in fifth grade at Maple Elementary School that are girls

Tell whether the statement is true or false. If false, give the reason. -15 ∉ {x|x is an even counting number}

Find n(A) for the set. -A = {800, 801, 802, . . ., 8000}

Express the set in roster form. -{x|x is a natural number multiple of 5}

Use $\subseteq, \nsubseteq, \subset$ , or both $\subset$ and $\subseteq$ to make a true statement. - $\{ \mathrm { s } , \mathrm { r } , \mathrm { t } \} ........ \{ \mathrm { s } , \mathrm { r } , \mathrm { t } \}$

Express the set in roster form. -The set of the days of the week

If the statement is true for all sets C and D, write ʺtrue.ʺ If it is not true for all sets C and D, write ʺfalse.ʺ Assume that $C \not = \varnothing$ ,and $C \subset U$ . - $\varnothing \subset \varnothing$

Use $\subseteq, \nsubseteq, \subset$ , or both $\subset$ and $\subseteq$ to make a true statement. - $\{ 6,7,8 \}$ ____ $\{ 6,7,8 \}$

Write a description of the set. -E = {x | x ∈ N and 2 < x ≤ 19}

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

Determine whether the set is well defined or not well defined. -The set of people who wear expensive clothes

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

Express the set in roster form. -The set of all whole numbers greater than 2 and less than 6

Express the set in roster form. -The set of seasons in a year

Critical Thinking Skills

Logic

Systems of Numeration

Number Theory and the Real Number System

Algebra, Graphs, and Functions

The Metric System

Geometry

Consumer Mathematics

Probability

Voting and Apportionment

Filters

Exam 2: Sets

Tell whether the statement is true or false. If false, give the reason. -{54, 55, 54, 55} = {54, 55}

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}. Determine whether the statement is true or false. -D ⊄ D

Determine whether the set is well defined or not well defined. -The set of rivers that flow south to north

Determine whether the set is well defined or not well defined. -The set of children in fifth grade at Maple Elementary School that are girls

Tell whether the statement is true or false. If false, give the reason. -15 ∉ {x|x is an even counting number}

Find n(A) for the set. -A = {800, 801, 802, . . ., 8000}

Express the set in roster form. -{x|x is a natural number multiple of 5}

Use ⊆,⊈,⊂ \subseteq, \nsubseteq, \subset ⊆,⊈,⊂ , or both ⊂ \subset ⊂ and ⊆ \subseteq⊆ to make a true statement. - {s,r,t}........{s,r,t}\{ \mathrm { s } , \mathrm { r } , \mathrm { t } \} ........ \{ \mathrm { s } , \mathrm { r } , \mathrm { t } \}{s,r,t}........{s,r,t}

Express the set in roster form. -The set of the days of the week

If the statement is true for all sets C and D, write ʺtrue.ʺ If it is not true for all sets C and D, write ʺfalse.ʺ Assume that C≠∅ C \not = \varnothing C=∅ ,and C⊂U C \subset UC⊂U . - ∅⊂∅ \varnothing \subset \varnothing ∅⊂∅

Use ⊆,⊈,⊂ \subseteq, \nsubseteq, \subset ⊆,⊈,⊂ , or both ⊂ \subset ⊂ and ⊆ \subseteq⊆ to make a true statement. - {6,7,8}\{ 6,7,8 \}{6,7,8} ____ {6,7,8}\{ 6,7,8 \}{6,7,8}

Write a description of the set. -E = {x | x ∈ N and 2 < x ≤ 19}

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

Determine whether the set is well defined or not well defined. -The set of people who wear expensive clothes

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

Express the set in roster form. -The set of all whole numbers greater than 2 and less than 6

Express the set in roster form. -The set of seasons in a year

Critical Thinking Skills

Logic

Systems of Numeration

Number Theory and the Real Number System

Algebra, Graphs, and Functions

The Metric System

Geometry

Consumer Mathematics

Probability

Voting and Apportionment

Filters

Use $\subseteq, \nsubseteq, \subset$ , or both $\subset$ and $\subseteq$ to make a true statement. - $\{ \mathrm { s } , \mathrm { r } , \mathrm { t } \} ........ \{ \mathrm { s } , \mathrm { r } , \mathrm { t } \}$

If the statement is true for all sets C and D, write ʺtrue.ʺ If it is not true for all sets C and D, write ʺfalse.ʺ Assume that $C \not = \varnothing$ ,and $C \subset U$ . - $\varnothing \subset \varnothing$

Use $\subseteq, \nsubseteq, \subset$ , or both $\subset$ and $\subseteq$ to make a true statement. - $\{ 6,7,8 \}$ ____ $\{ 6,7,8 \}$