Question 1

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

Accepted Answer

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

Question 2

Find n(A)for the set.
-A = {700, 701, 702, ..., 7000}

Accepted Answer

A) n(
A) = 6301 
B) n(
A) = 4 
C) n(
A) = 6300 
D) n(
A) = 7000 
A) n(
A) = 6301 
B) n(
A) = 4 
C) n(
A) = 6300 
D) n(
A) = 7000

Question 3

List the elements in the set.
-$\{ x \mid x$ is a counting number less than $- 2 \}$

Accepted Answer

A)  $\{ \ldots , - 5 , - 4 , - 3 \}$ 
B)  $\{ - 1,0,1 , \ldots \}$ 
C)  $\{ - 3 , - 4 , - 5 , \ldots \}$ 
D)  $\varnothing$ 
A)  $\{ \ldots , - 5 , - 4 , - 3 \}$ 
B)  $\{ - 1,0,1 , \ldots \}$ 
C)  $\{ - 3 , - 4 , - 5 , \ldots \}$ 
D)  $\varnothing$

Question 4

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

Accepted Answer

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

Question 5

Complete the blank with either $\in$ or $\notin$ to make the statement true.
-$5 \ldots \{ 3,4,5,6 \}$

Accepted Answer

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

Question 6

Tell whether the statement is true or false.
-$17 \notin \{ 16,14,13 , \ldots , 1 \}$

Accepted Answer

A) True 
 B)False

Question 7

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets.
-{0, 9, 12, 16} and {9, 12, 16}

Accepted Answer

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

Question 8

Tell whether the statement is true or false.
-$9 \in \{ 18,27,36,45,54 \}$

Accepted Answer

A) True 
 B)False

Question 9

Find the cardinal number of the set.
-{Monday, Tuesday, ..., Saturday}

Accepted Answer

A)  7 
B)  3 
C)  4 
D)  6 
A)  7 
B)  3 
C)  4 
D)  6

Question 10

Find the cardinal number of the indicated set. Use the cardinal number formula.
-If $n ( A ) = 8 , n ( B ) = 21$ and $n ( A \cup B ) = 25$, what is $n ( A \cap B )$ ?

Accepted Answer

A)  4 
B)  12 
C)  6 
D)  2 
A)  4 
B)  12 
C)  6 
D)  2

Question 11

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

Accepted Answer

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

Question 12

Write the set in set-builder notation.
-$\{ 4 \}$

Accepted Answer

A)  $\{ x \mid x$ is the natural number $4 \}$ 
B)  $\{ x \mid x$ is a natural number $\}$ 
C)  $\{ x \}$ 
D)  $\{ x$ is a constant $\}$ 
A)  $\{ x \mid x$ is the natural number $4 \}$ 
B)  $\{ x \mid x$ is a natural number $\}$ 
C)  $\{ x \}$ 
D)  $\{ x$ is a constant $\}$

Question 13

Identify the set as finite or infinite.
-{7, 8, 9, ..., 28}

Accepted Answer

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

Question 14

Tell whether the statement is true or false.
-{s, q, y, o, d} = {o, d, q, s, y}

Accepted Answer

A) True 
 B)False

Question 15

List the elements in the set.
-$\{ x \mid x$ is a whole number between 6 and $10 \}$

Accepted Answer

A)  $\{ 6,7,8,9 \}$ 
B)  $\{ 7,8,9 \}$ 
C)  $\{ 7,8,9,10 \}$ 
D)  $\{ 6,7,8,9,10 \}$ 
A)  $\{ 6,7,8,9 \}$ 
B)  $\{ 7,8,9 \}$ 
C)  $\{ 7,8,9,10 \}$ 
D)  $\{ 6,7,8,9,10 \}$

Question 16

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

Accepted Answer

A)  $\varnothing$' 
B)  $\{ 0 \}$ 
C)  $U$ 
D)  $\varnothing$ 
A)  $\varnothing$' 
B)  $\{ 0 \}$ 
C)  $U$ 
D)  $\varnothing$

Question 17

Complete the blank with either $\in$ or $\notin$ to make the statement true.
-$\{ 8 \}.... \{ \{ 5 \} , \{ 6 \} , \{ 7 \} , \{ 8 \} , \{ 9 \} \}$

Accepted Answer

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

Question 18

Draw an appropriate Venn diagram and use the given information to fill in the number of elements in each region.
-$$n ( A ) = 14 , n ( B ) = 21 , n ( A \cup B ) = 25 , n \left( B ^ { \prime } \right) = 9$$

Accepted Answer

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

Question 19

Complete the blank with either $\in$ or $\notin$ to make the statement true.
-$4 ..... \{ 5 + 5,3 + 5,1 + 5 , - 1 + 5 \}$

Accepted Answer

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

Question 20

Find the number of proper subsets of the set.
-{0}

Accepted Answer

A) 2 
B) 4 
C) 0 
D) 1 
A) 2 
B) 4 
C) 0 
D) 1

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

Find n(A)for the set. -A = {700, 701, 702, ..., 7000}

List the elements in the set. - $\{ x \mid x$ is a counting number less than $- 2 \}$

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $5 \ldots \{ 3,4,5,6 \}$

Tell whether the statement is true or false. - $17 \notin \{ 16,14,13 , \ldots , 1 \}$

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets. -{0, 9, 12, 16} and {9, 12, 16}

Tell whether the statement is true or false. - $9 \in \{ 18,27,36,45,54 \}$

Find the cardinal number of the set. -{Monday, Tuesday, ..., Saturday}

Find the cardinal number of the indicated set. Use the cardinal number formula. -If $n ( A ) = 8 , n ( B ) = 21$ and $n ( A \cup B ) = 25$ , what is $n ( A \cap B )$ ?

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

Write the set in set-builder notation. - $\{ 4 \}$

Identify the set as finite or infinite. -{7, 8, 9, ..., 28}

Tell whether the statement is true or false. -{s, q, y, o, d} = {o, d, q, s, y}

List the elements in the set. - $\{ x \mid x$ is a whole number between 6 and $10 \}$

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

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $\{ 8 \}.... \{ \{ 5 \} , \{ 6 \} , \{ 7 \} , \{ 8 \} , \{ 9 \} \}$

Draw an appropriate Venn diagram and use the given information to fill in the number of elements in each region. - $n ( A ) = 14 , n ( B ) = 21 , n ( A \cup B ) = 25 , n \left( B ^ { \prime } \right) = 9$

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $4 ..... \{ 5 + 5,3 + 5,1 + 5 , - 1 + 5 \}$

Find the number of proper subsets of the set. -{0}

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∩(B∪C)A \cap ( B \cup C )A∩(B∪C)

Find n(A)for the set. -A = {700, 701, 702, ..., 7000}

List the elements in the set. - {x∣x\{ x \mid x{x∣x is a counting number less than −2}- 2 \}−2}

Complete the blank with either ∈\in∈ or ∉\notin∈/ to make the statement true. - 5…{3,4,5,6}5 \ldots \{ 3,4,5,6 \}5…{3,4,5,6}

Tell whether the statement is true or false. - 17∉{16,14,13,…,1}17 \notin \{ 16,14,13 , \ldots , 1 \}17∈/{16,14,13,…,1}

Decide whether or not it is possible to set up a one-to-one correspondence between the elements of the sets. -{0, 9, 12, 16} and {9, 12, 16}

Tell whether the statement is true or false. - 9∈{18,27,36,45,54}9 \in \{ 18,27,36,45,54 \}9∈{18,27,36,45,54}

Find the cardinal number of the set. -{Monday, Tuesday, ..., Saturday}

Find the cardinal number of the indicated set. Use the cardinal number formula. -If n(A)=8,n(B)=21n ( A ) = 8 , n ( B ) = 21n(A)=8,n(B)=21 and n(A∪B)=25n ( A \cup B ) = 25n(A∪B)=25 , what is n(A∩B)n ( A \cap B )n(A∩B) ?

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

Write the set in set-builder notation. - {4}\{ 4 \}{4}

Identify the set as finite or infinite. -{7, 8, 9, ..., 28}

Tell whether the statement is true or false. -{s, q, y, o, d} = {o, d, q, s, y}

List the elements in the set. - {x∣x\{ x \mid x{x∣x is a whole number between 6 and 10}10 \}10}

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

Complete the blank with either ∈\in∈ or ∉\notin∈/ to make the statement true. - {8}....{{5},{6},{7},{8},{9}}\{ 8 \}.... \{ \{ 5 \} , \{ 6 \} , \{ 7 \} , \{ 8 \} , \{ 9 \} \}{8}....{{5},{6},{7},{8},{9}}

Draw an appropriate Venn diagram and use the given information to fill in the number of elements in each region. - n(A)=14,n(B)=21,n(A∪B)=25,n(B′)=9n ( A ) = 14 , n ( B ) = 21 , n ( A \cup B ) = 25 , n \left( B ^ { \prime } \right) = 9n(A)=14,n(B)=21,n(A∪B)=25,n(B′)=9

Complete the blank with either ∈\in∈ or ∉\notin∈/ to make the statement true. - 4.....{5+5,3+5,1+5,−1+5}4 ..... \{ 5 + 5,3 + 5,1 + 5 , - 1 + 5 \}4.....{5+5,3+5,1+5,−1+5}

Find the number of proper subsets of the set. -{0}

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 =\{,,,,,,,,,\} =\{,,,,\} =\{,,,\} =\{,,,,\} - $A \cap ( B \cup C )$

List the elements in the set. - $\{ x \mid x$ is a counting number less than $- 2 \}$

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $5 \ldots \{ 3,4,5,6 \}$

Tell whether the statement is true or false. - $17 \notin \{ 16,14,13 , \ldots , 1 \}$

Tell whether the statement is true or false. - $9 \in \{ 18,27,36,45,54 \}$

Find the cardinal number of the indicated set. Use the cardinal number formula. -If $n ( A ) = 8 , n ( B ) = 21$ and $n ( A \cup B ) = 25$ , what is $n ( A \cap B )$ ?

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

Write the set in set-builder notation. - $\{ 4 \}$

List the elements in the set. - $\{ x \mid x$ is a whole number between 6 and $10 \}$

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

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $\{ 8 \}.... \{ \{ 5 \} , \{ 6 \} , \{ 7 \} , \{ 8 \} , \{ 9 \} \}$

Draw an appropriate Venn diagram and use the given information to fill in the number of elements in each region. - $n ( A ) = 14 , n ( B ) = 21 , n ( A \cup B ) = 25 , n \left( B ^ { \prime } \right) = 9$

Complete the blank with either $\in$ or $\notin$ to make the statement true. - $4 ..... \{ 5 + 5,3 + 5,1 + 5 , - 1 + 5 \}$