Question 1

Tell whether the statement is true or false.
-$9 \notin \{ x \mid x \text { is an even counting number } \}$

Accepted Answer

A) True 
 B)False

Question 2

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.
-$L ^ { \prime } \cap \mathrm { A }$

Accepted Answer

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

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

Identify the set as finite or infinite.
-$\{ x \mid x$ is an odd counting number $\}$

Accepted Answer

A)  Finite 
B)  Infinite 
A)  Finite 
B)  Infinite

Question 5

Complete the blank with either $\in$ or $\notin$ to make the statement true.
-$0 ...\ldots \{ - 1,1,3,16,26 \}$

Accepted Answer

A)  $\notin$ 
B)  $\in$ 
A)  $\notin$ 
B)  $\in$

Question 6

Solve the problem.
-A survey of 280 families showed that 107 had a dog;
82 had a cat;
37 had a dog and a cat;
105 had neither a cat nor a dog nor a parakeet;
9 had a cat, a dog, and a parakeet.
How many had a parakeet only?

Accepted Answer

A) 33 
B) 38 
C) 28 
D) 23 
A) 33 
B) 38 
C) 28 
D) 23

Question 7

Write the set in set-builder notation.
-$\{ 2,4,8,16,32 , \ldots \}$

Accepted Answer

A)  $\{ x \mid x$ is a positive multiple of $2 \}$ 
B)  $\{ x \mid x$ is a positive multiple of $4 \}$ 
C)  $\{ x \mid x$ is a positive integer power of $2 \}$ 
D)  $\{ x \mid x$ is an integer power of $2 \}$ 
A)  $\{ x \mid x$ is a positive multiple of $2 \}$ 
B)  $\{ x \mid x$ is a positive multiple of $4 \}$ 
C)  $\{ x \mid x$ is a positive integer power of $2 \}$ 
D)  $\{ x \mid x$ is an integer power of $2 \}$

Question 8

Identify the set as finite or infinite.
-$\{ x \mid x$ is a 12-headed lizard $\}$

Accepted Answer

A)  Infinite 
B)  Finite 
A)  Infinite 
B)  Finite

Question 9

Determine whether or not the set is well defined.
-$\{ x \mid x$ is a four-year college in Utah $\}$

Accepted Answer

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

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

Accepted Answer

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

Question 11

Find the cardinal number of the set.
-The numbers in the Venn Diagram below represent cardinalities.  
Find $n ( A \cup B )$.

Accepted Answer

A)  4 
B)  48 
C)  52 
D)  24 
A)  4 
B)  48 
C)  52 
D)  24

Question 12

Find the number of subsets of the set.
-{5, 6, 7}

Accepted Answer

A) 3 
B) 6 
C) 8 
D) 7 
A) 3 
B) 6 
C) 8 
D) 7

Question 13

Determine whether or not the set is well defined.
-$\{ x \mid x$ is a tennis player who has won at Wimbledon $\}$

Accepted Answer

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

Question 14

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 L and K'

Accepted Answer

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

Question 15

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.
-$A \cap B \cap D$

Accepted Answer

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

Question 16

Tell whether the statement is true or false.
-(12 - 8, 16 - 11)= (4, 5)

Accepted Answer

A) True 
 B)False

Question 17

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

Accepted Answer

A) {1, 2, 3, b, d} 
B) {b, d, 1, 2, 3} 
C) {1, 2, b, d} 
D) {1, 2, b, c, d} 
A) {1, 2, 3, b, d} 
B) {b, d, 1, 2, 3} 
C) {1, 2, b, d} 
D) {1, 2, b, c, d}

Question 18

Find the number of proper subsets of the set.
-{7, 8, 9}

Accepted Answer

A) 2 
B) 5 
C) 6 
D) 7 
A) 2 
B) 5 
C) 6 
D) 7

Question 19

Solve the problem.
-An adventure travel company has reservations from four people (Lee, Maria, Nancy, and Pablo)for its white water rafting trip on June 1st. However the company knows that any of these people may Fail to show up on the day of the trip. Denoting these four people by l, m, n, p, list all possibilities
For the group of people who show up on June 1st for the rafting trip (ie list all possible subsets of
{l, m, n, p}).

Accepted Answer

A)  $\{ 1 \} , \{ m \} , \{ n \} , \{ p \} , \{ 1 , m \} , \{ 1 , n \} , \{ 1 , p \} , \{ m , n \} , \{ m , p \} , \{ n , p \} , \{ 1 , m , n \} , \{ 1 , m , p \} , \{ 1 , n , p \} , \{ m , n , p \} , \{ m$, $\mathrm { n } , 1 \} , \{ 1 , \mathrm {~m} , \mathrm { n } , \mathrm { p } \}$ 
B)  $\varnothing , \{ 1 \} , \{ m \} , \{ n \} , \{ p \} , \{ 1 , m \} , \{ 1 , n \} , \{ m , n \} , \{ m , p \} , \{ n , p \} , \{ 1 , m , n \} , \{ 1 , m , p \} , \{ 1 , n , p \} , \{ m , n , p \}$ 
C)  $\varnothing , \{ 1 \} , \{ m \} , \{ n \} , \{ p \} , \{ 1 , m \} , \{ 1 , n \} , \{ 1 , p \} , \{ m , n \} , \{ m , p \} , \{ n , p \} , \{ 1 , m , n \} , \{ 1 , m , p \} , \{ 1 , n , p \} , \{ m , n , p \}$, $\{ 1 , m , n , p \}$ 
D)  $\{ 1 \} , \{ m \} , \{ n \} , \{ p \} , \{ 1 , m \} , \{ 1 , n \} , \{ 1 , p \} , \{ m , n \} , \{ m , p \} , \{ n , p \} , \{ 1 , m , n \} , \{ 1 , m , p \} , \{ 1 , n , p \} , \{ m , n , p \} , \{ 1$, $\mathrm { m } , \mathrm { n } , \mathrm { p }$ 
A)  $\{ 1 \} , \{ m \} , \{ n \} , \{ p \} , \{ 1 , m \} , \{ 1 , n \} , \{ 1 , p \} , \{ m , n \} , \{ m , p \} , \{ n , p \} , \{ 1 , m , n \} , \{ 1 , m , p \} , \{ 1 , n , p \} , \{ m , n , p \} , \{ m$, $\mathrm { n } , 1 \} , \{ 1 , \mathrm {~m} , \mathrm { n } , \mathrm { p } \}$ 
B)  $\varnothing , \{ 1 \} , \{ m \} , \{ n \} , \{ p \} , \{ 1 , m \} , \{ 1 , n \} , \{ m , n \} , \{ m , p \} , \{ n , p \} , \{ 1 , m , n \} , \{ 1 , m , p \} , \{ 1 , n , p \} , \{ m , n , p \}$ 
C)  $\varnothing , \{ 1 \} , \{ m \} , \{ n \} , \{ p \} , \{ 1 , m \} , \{ 1 , n \} , \{ 1 , p \} , \{ m , n \} , \{ m , p \} , \{ n , p \} , \{ 1 , m , n \} , \{ 1 , m , p \} , \{ 1 , n , p \} , \{ m , n , p \}$, $\{ 1 , m , n , p \}$ 
D)  $\{ 1 \} , \{ m \} , \{ n \} , \{ p \} , \{ 1 , m \} , \{ 1 , n \} , \{ 1 , p \} , \{ m , n \} , \{ m , p \} , \{ n , p \} , \{ 1 , m , n \} , \{ 1 , m , p \} , \{ 1 , n , p \} , \{ m , n , p \} , \{ 1$, $\mathrm { m } , \mathrm { n } , \mathrm { p }$

Question 20

Find the cardinal number of the set.
-$\{ - 4 , - 8 , - 12 , - 16 , \ldots . . \}$

Accepted Answer

A)    
B)  100 
C)  4 
D)  $\mathrm { C }$ 
A)    
B)  100 
C)  4 
D)  $\mathrm { C }$

Tell whether the statement is true or false. - $9 \notin \{ x \mid x \text { is an even counting number } \}$

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

Identify the set as finite or infinite. - $\{ x \mid x$ is an odd counting number $\}$

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $0 ...\ldots \{ - 1,1,3,16,26 \}$

Solve the problem. -A survey of 280 families showed that 107 had a dog; 82 had a cat; 37 had a dog and a cat; 105 had neither a cat nor a dog nor a parakeet; 9 had a cat, a dog, and a parakeet. How many had a parakeet only?

Write the set in set-builder notation. - $\{ 2,4,8,16,32 , \ldots \}$

Identify the set as finite or infinite. - $\{ x \mid x$ is a 12-headed lizard $\}$

Determine whether or not the set is well defined. - $\{ x \mid x$ is a four-year college in Utah $\}$

Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. $Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. Find n ( A \cup B ) .$ Find $n ( A \cup B )$ .

Find the number of subsets of the set. -{5, 6, 7}

Determine whether or not the set is well defined. - $\{ x \mid x$ is a tennis player who has won at Wimbledon $\}$

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. - $A \cap B \cap D$

Tell whether the statement is true or false. -(12 - 8, 16 - 11)= (4, 5)

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

Find the number of proper subsets of the set. -{7, 8, 9}

Find the cardinal number of the set. - $\{ - 4 , - 8 , - 12 , - 16 , \ldots . . \}$

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

Tell whether the statement is true or false. - 9∉{x∣x is an even counting number }9 \notin \{ x \mid x \text { is an even counting number } \}9∈/{x∣x is an even counting number }

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

Identify the set as finite or infinite. - {x∣x\{ x \mid x{x∣x is an odd counting number }\}}

Complete the blank with either ∈\in∈ or ∉\notin∈/ to make the statement true. - 0...…{−1,1,3,16,26}0 ...\ldots \{ - 1,1,3,16,26 \}0...…{−1,1,3,16,26}

Solve the problem. -A survey of 280 families showed that 107 had a dog; 82 had a cat; 37 had a dog and a cat; 105 had neither a cat nor a dog nor a parakeet; 9 had a cat, a dog, and a parakeet. How many had a parakeet only?

Write the set in set-builder notation. - {2,4,8,16,32,…}\{ 2,4,8,16,32 , \ldots \}{2,4,8,16,32,…}

Identify the set as finite or infinite. - {x∣x\{ x \mid x{x∣x is a 12-headed lizard }\}}

Determine whether or not the set is well defined. - {x∣x\{ x \mid x{x∣x is a four-year college in Utah }\}}

Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. Find n(A∪B)n ( A \cup B )n(A∪B) .

Find the number of subsets of the set. -{5, 6, 7}

Determine whether or not the set is well defined. - {x∣x\{ x \mid x{x∣x is a tennis player who has won at Wimbledon }\}}

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∩B∩DA \cap B \cap DA∩B∩D

Tell whether the statement is true or false. -(12 - 8, 16 - 11)= (4, 5)

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

Find the number of proper subsets of the set. -{7, 8, 9}

Find the cardinal number of the set. - {−4,−8,−12,−16,…..}\{ - 4 , - 8 , - 12 , - 16 , \ldots . . \}{−4,−8,−12,−16,…..}

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

Tell whether the statement is true or false. - $9 \notin \{ x \mid x \text { is an even counting number } \}$

Identify the set as finite or infinite. - $\{ x \mid x$ is an odd counting number $\}$

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $0 ...\ldots \{ - 1,1,3,16,26 \}$

Write the set in set-builder notation. - $\{ 2,4,8,16,32 , \ldots \}$

Identify the set as finite or infinite. - $\{ x \mid x$ is a 12-headed lizard $\}$

Determine whether or not the set is well defined. - $\{ x \mid x$ is a four-year college in Utah $\}$

Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. $Find the cardinal number of the set. -The numbers in the Venn Diagram below represent cardinalities. Find n ( A \cup B ) .$ Find $n ( A \cup B )$ .

Determine whether or not the set is well defined. - $\{ x \mid x$ is a tennis player who has won at Wimbledon $\}$

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. - $A \cap B \cap D$

Find the cardinal number of the set. - $\{ - 4 , - 8 , - 12 , - 16 , \ldots . . \}$