Question 1

Consider the sets. $A =$ {letters in the word pills } $B =$ {6} $C =$ $\{ p , i , e \}$ $D =$ $\{ 2 + 1 \}$ $E =$ {three} $F =$ {3} Which of the sets can be placed into a one-to-one correspondence with $D$ ?

Accepted Answer

A)  $D \leftrightarrow B \leftrightarrow E \leftrightarrow F$ 
B)  $D \leftrightarrow A \leftrightarrow E$ 
C)  $D \leftrightarrow A$ 
D)  $D \leftrightarrow B$ 
E)  $D \leftrightarrow B \leftrightarrow F$ 
A)  $D \leftrightarrow B \leftrightarrow E \leftrightarrow F$ 
B)  $D \leftrightarrow A \leftrightarrow E$ 
C)  $D \leftrightarrow A$ 
D)  $D \leftrightarrow B$ 
E)  $D \leftrightarrow B \leftrightarrow F$ A

Question 2

Draw a Venn diagram showing the sets $A$ $B$ and $C$ where $A$ is the set of people in a classroom with blue eyes, $B$ is the set of people in the classroom with black shoes, $C$ is the set of people in the classroom with wedding rings, and the universe is the set of people in the classroom. Assume that each region corresponds to a nonempty set.

Accepted Answer

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

Question 3

Write the negation of the statement. 
All cats have fleas.

Accepted Answer

Some cats do not have fleas.

Question 4

In a recent survey of $100$ women, the information was gathered: $59$ use shampoo A. $52$ use shampoo B. $32$ use shampoo C. $23$ use shampoos A and B. $19$ use shampoos A and C. $12$ use shampoos B and C. $11$ use all three. How many are not using any of the three listed shampoos (Region VIII)? A = {women who use shampoo A } B = {women who use shampoo B } C = {women who use shampoo C } Use the figure (with Regions I to VIII) to answer the question.   __________ women

Accepted Answer

The answer of In a recent survey of $100$ women,...

Question 5

How many subsets does the set $\{ a , e , i , c , u \}$ have?

Accepted Answer

The answer of How many subsets does the set \(\{...

Question 6

Draw a Venn diagram showing the sets $A$ $B$ and $C$ where $A$ is the set of natural numbers, $B$ is the set of integers, $C$ is the set of rational numbers, and the universe is the set of real numbers. Assume that each region corresponds to a nonempty set.

Accepted Answer

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

Question 7

Let $$\begin{array} { l } 
U = \{ 1,2,3,4,5,6,7,8,9,10 \} \
A = \{ 2,4,6,8 \} \
B = \{ 5,7 \} \
C = \{ 2,5,6,7,10 \}
\end{array}$$ List all the members of the set. $A \cap ( B \cap \bar { C } )$

Accepted Answer

A)  $\{ 1,5 \}$ 
B)  $\{ 2,6 \}$ 
C)  $( 5,7 )$ 
D)  $\{ 2,4,6,8 \}$ 
E)  $\varnothing$ 
A)  $\{ 1,5 \}$ 
B)  $\{ 2,6 \}$ 
C)  $( 5,7 )$ 
D)  $\{ 2,4,6,8 \}$ 
E)  $\varnothing$

Question 8

In a recent survey of $100$ women, the following information was gathered: $58$ use shampoo A. $51$ use shampoo B. $32$ use shampoo C. $21$ use shampoos A and B. $19$ use shampoos A and C. $14$ use shampoos B and C. $12$ use all three. How many are using shampoo C only (Region III)? A = {women who use shampoo A } B = {women who use shampoo B } C = {women who use shampoo C } Use the figure (with Regions I to VIII) to answer the question.   __________ women

Accepted Answer

The answer of In a recent survey of $100$ women,...

Question 9

Let $$\begin{array} { l } 
U = \{ 1,2,3,4,5,6,7,8,9,10 \} \
A = \{ 2,4,6,8 \} \
B = \{ 5,7 \} \
C = \{ 2,5,6,7,10 \}
\end{array}$$ List all the members of the set. $$A \cap \overline { B \cup C }$$

Accepted Answer

The answer of Let \[\begin{array} { l } 
U =...

Question 10

Specify the set by roster. 
{letters in the word son }

Accepted Answer

The answer of Specify the set by roster. 
{letters in...

Question 11

If $\varnothing$ has a cardinality, what is it? Explain.

Accepted Answer

@#LAT-DLM& has a cardinality o

Question 12

In a recent survey of $100$ women, the following information was gathered: $54$ use shampoo A. $52$ use shampoo B. $35$ use shampoo C. $22$ use shampoos A and B. $18$ use shampoos A and C. $13$ use shampoos B and C. $12$ use all three. Name the three sets in this survey A , B , and C . Use the figure (with Regions I through VIII) to answer the question.

Accepted Answer

A)  A = {women who use shampoo B } B = {women who use shampoos A and C}
C = {women who use all three} 
B)  A = {women who use shampoo A} B = {women who use shampoo B}
C = {women who use shampoo C} 
C)  A = {women who use shampoo A, but not B or C} B = {women who use shampoo B, but not A or C}
C = {women who use shampoo C, but not A or B} 
D)  A = {women who use shampoo A, but not B and C} B = {women who use shampoo B, but not A and C}
C = {women who use shampoo A, but not B and C} 
E)  A = {women who use shampoo A, but not B} B = {women who use shampoo B, but not A}
C = {women who use shampoo C, but not A} 
A)  A = {women who use shampoo B } B = {women who use shampoos A and C}
C = {women who use all three} 
B)  A = {women who use shampoo A} B = {women who use shampoo B}
C = {women who use shampoo C} 
C)  A = {women who use shampoo A, but not B or C} B = {women who use shampoo B, but not A or C}
C = {women who use shampoo C, but not A or B} 
D)  A = {women who use shampoo A, but not B and C} B = {women who use shampoo B, but not A and C}
C = {women who use shampoo A, but not B and C} 
E)  A = {women who use shampoo A, but not B} B = {women who use shampoo B, but not A}
C = {women who use shampoo C, but not A}

Question 13

Let $$\begin{array} { l } 
U = \{ 1,2,3,4,5,6,7 \} \
A = \{ 4,5,6,7 \} \
B = \{ 2,3,5,7 \} \
C = \{ 4,6,7 \}
\end{array}$$ List all the members of the set. $\bar { A }$

Accepted Answer

A)  $\{ 1,2,3,4,5,6,7 \}$ 
B)  $\{ 4,5,6,7 \}$ 
C)  $\{ 1,2,3 \}$ 
D)  $\{ 1,4,6 \}$ 
E)  $\varnothing$ 
A)  $\{ 1,2,3,4,5,6,7 \}$ 
B)  $\{ 4,5,6,7 \}$ 
C)  $\{ 1,2,3 \}$ 
D)  $\{ 1,4,6 \}$ 
E)  $\varnothing$

Question 14

Translate the given statement into words. $\sim ( p \vee q )$ Let p: Lizards have a shell; q: Lizards eat bugs.

Accepted Answer

A)  It is not the case that Lizards have a shell or Lizards eat bugs. 
B)  Lizards have a shell and Lizards do not eat bugs. 
C)  Lizards do not have a shell and Lizards eat bugs. 
D)  Lizards do not have a shell or Lizards eat bugs. 
E)  It is not the case that Lizards have a shell and Lizards eat bugs. 
A)  It is not the case that Lizards have a shell or Lizards eat bugs. 
B)  Lizards have a shell and Lizards do not eat bugs. 
C)  Lizards do not have a shell and Lizards eat bugs. 
D)  Lizards do not have a shell or Lizards eat bugs. 
E)  It is not the case that Lizards have a shell and Lizards eat bugs.

Question 15

Give the numbers of elements in the region marked I in the figure. $| U | = 500 , | A | = 160 , | B | = 170 , | C | = 65 , | A \cap B | = 20$ $$| A \cap C | = 55 , | B \cap C | = 20 , | A \cap B \cap C | = 20$$

Accepted Answer

A)  150 elements 
B)  0 elements 
C)  160 elements 
D)  10 elements 
E)  105 elements 
A)  150 elements 
B)  0 elements 
C)  160 elements 
D)  10 elements 
E)  105 elements

Question 16

Let $$\begin{array} { l } 
U = \{ 1,2,3,4,5,6,7 \} \
A = \{ 1,2,4,5 \} \
B = \{ 1,2,3,6 \} \
C = \{ 4,6,7 \}
\end{array}$$ List all the members of the set. $A \cup B$

Accepted Answer

A)  $\{ 1,2,3,6 \}$ 
B)  $\{ 1,2,4,5 \}$ 
C)  $\{ 1,2 \}$ 
D)  $\{ 1,2,3,4,5,6 \}$ 
E)  $\varnothing$ 
A)  $\{ 1,2,3,6 \}$ 
B)  $\{ 1,2,4,5 \}$ 
C)  $\{ 1,2 \}$ 
D)  $\{ 1,2,3,4,5,6 \}$ 
E)  $\varnothing$

Question 17

Draw a Venn diagram showing the sets $A$ $B$ and $C$ where $A$ is the set of flowers, $B$ is the set of flagpoles, $6$ is the set of pencils, and the universe is the set of objects. Assume that each region corresponds to a nonempty set.

Accepted Answer

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

Question 18

How many subsets are there in a set with $p$ elements?

Accepted Answer

The answer of How many subsets are there in a...

Question 19

Let $$\begin{array} { l } 
U = \{ 1,2,3,4,5,6,7,8,9,10 \} \
A = \{ 2,3,5,6,7 \} \
B = \{ 4,5,6,7,8 \}
\end{array}$$ List all the members of the set. $\bar { A }$

Accepted Answer

The answer of Let \[\begin{array} { l } 
U =...

Question 20

Do the following sets have the same cardinality? 
{48, 49, 50, ..., 818, 819} 
{485, 487, 489, ..., 1,969, 1,971} 
______________________________ 
( They have the same cardinality . / They do not have the same cardinality .)

Accepted Answer

They do no

Consider the sets. $A =$ {letters in the word pills } $B =$ {6} $C =$ $\{ p , i , e \}$ $D =$ $\{ 2 + 1 \}$ $E =$ {three} $F =$ {3} Which of the sets can be placed into a one-to-one correspondence with $D$ ?

Write the negation of the statement. All cats have fleas.

How many subsets does the set $\{ a , e , i , c , u \}$ have?

Draw a Venn diagram showing the sets $A$ $B$ and $C$ where $A$ is the set of natural numbers, $B$ is the set of integers, $C$ is the set of rational numbers, and the universe is the set of real numbers. Assume that each region corresponds to a nonempty set.

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{5,7\} C=\{2,5,6,7,10\} List all the members of the set. $A \cap ( B \cap \bar { C } )$

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{5,7\} C=\{2,5,6,7,10\} List all the members of the set. $A \cap \overline { B \cup C }$

Specify the set by roster. {letters in the word son }

If $\varnothing$ has a cardinality, what is it? Explain.

Let U=\{1,2,3,4,5,6,7\} A=\{4,5,6,7\} B=\{2,3,5,7\} C=\{4,6,7\} List all the members of the set. $\bar { A }$

Translate the given statement into words. $\sim ( p \vee q )$ Let p: Lizards have a shell; q: Lizards eat bugs.

Let U=\{1,2,3,4,5,6,7\} A=\{1,2,4,5\} B=\{1,2,3,6\} C=\{4,6,7\} List all the members of the set. $A \cup B$

Draw a Venn diagram showing the sets $A$ $B$ and $C$ where $A$ is the set of flowers, $B$ is the set of flagpoles, $6$ is the set of pencils, and the universe is the set of objects. Assume that each region corresponds to a nonempty set.

How many subsets are there in a set with $p$ elements?

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,3,5,6,7\} B=\{4,5,6,7,8\} List all the members of the set. $\bar { A }$

Do the following sets have the same cardinality? {48, 49, 50, ..., 818, 819} {485, 487, 489, ..., 1,969, 1,971} ______________________________ ( They have the same cardinality . / They do not have the same cardinality .)

Arithmetic, Calculators, and Problem Solving

Sets of Numbers

Introduction to Algebra

Percents and Problem Solving

Introduction to Geometry

Measurement and Problem Solving

Applications of Percent

Probability

Statistics

Graphs

Filters

Exam 8: Sets and Logic

Consider the sets. A=A =A= {letters in the word pills } B=B =B= {6} C=C =C= {p,i,e}\{ p , i , e \}{p,i,e} D=D =D= {2+1}\{ 2 + 1 \}{2+1} E=E =E= {three} F=F =F= {3} Which of the sets can be placed into a one-to-one correspondence with DDD ?

Write the negation of the statement. All cats have fleas.

How many subsets does the set {a,e,i,c,u}\{ a , e , i , c , u \}{a,e,i,c,u} have?

Draw a Venn diagram showing the sets AAA BBB and CCC where AAA is the set of natural numbers, BBB is the set of integers, CCC is the set of rational numbers, and the universe is the set of real numbers. Assume that each region corresponds to a nonempty set.

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{5,7\} C=\{2,5,6,7,10\} List all the members of the set. A∩(B∩Cˉ)A \cap ( B \cap \bar { C } )A∩(B∩Cˉ)

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{5,7\} C=\{2,5,6,7,10\} List all the members of the set. A∩B∪C‾A \cap \overline { B \cup C }A∩B∪C

Specify the set by roster. {letters in the word son }

If ∅\varnothing∅ has a cardinality, what is it? Explain.

Let U=\{1,2,3,4,5,6,7\} A=\{4,5,6,7\} B=\{2,3,5,7\} C=\{4,6,7\} List all the members of the set. Aˉ\bar { A }Aˉ

Translate the given statement into words. ∼(p∨q)\sim ( p \vee q )∼(p∨q) Let p: Lizards have a shell; q: Lizards eat bugs.

Let U=\{1,2,3,4,5,6,7\} A=\{1,2,4,5\} B=\{1,2,3,6\} C=\{4,6,7\} List all the members of the set. A∪BA \cup BA∪B

Draw a Venn diagram showing the sets AAA BBB and CCC where AAA is the set of flowers, BBB is the set of flagpoles, 666 is the set of pencils, and the universe is the set of objects. Assume that each region corresponds to a nonempty set.

How many subsets are there in a set with ppp elements?

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,3,5,6,7\} B=\{4,5,6,7,8\} List all the members of the set. Aˉ\bar { A }Aˉ

Do the following sets have the same cardinality? {48, 49, 50, ..., 818, 819} {485, 487, 489, ..., 1,969, 1,971} ______________________________ ( They have the same cardinality . / They do not have the same cardinality .)

Arithmetic, Calculators, and Problem Solving

Sets of Numbers

Introduction to Algebra

Percents and Problem Solving

Introduction to Geometry

Measurement and Problem Solving

Applications of Percent

Probability

Statistics

Graphs

Filters

Consider the sets. $A =$ {letters in the word pills } $B =$ {6} $C =$ $\{ p , i , e \}$ $D =$ $\{ 2 + 1 \}$ $E =$ {three} $F =$ {3} Which of the sets can be placed into a one-to-one correspondence with $D$ ?

How many subsets does the set $\{ a , e , i , c , u \}$ have?

Draw a Venn diagram showing the sets $A$ $B$ and $C$ where $A$ is the set of natural numbers, $B$ is the set of integers, $C$ is the set of rational numbers, and the universe is the set of real numbers. Assume that each region corresponds to a nonempty set.

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{5,7\} C=\{2,5,6,7,10\} List all the members of the set. $A \cap ( B \cap \bar { C } )$

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,4,6,8\} B=\{5,7\} C=\{2,5,6,7,10\} List all the members of the set. $A \cap \overline { B \cup C }$

If $\varnothing$ has a cardinality, what is it? Explain.

Let U=\{1,2,3,4,5,6,7\} A=\{4,5,6,7\} B=\{2,3,5,7\} C=\{4,6,7\} List all the members of the set. $\bar { A }$

Translate the given statement into words. $\sim ( p \vee q )$ Let p: Lizards have a shell; q: Lizards eat bugs.

Let U=\{1,2,3,4,5,6,7\} A=\{1,2,4,5\} B=\{1,2,3,6\} C=\{4,6,7\} List all the members of the set. $A \cup B$

Draw a Venn diagram showing the sets $A$ $B$ and $C$ where $A$ is the set of flowers, $B$ is the set of flagpoles, $6$ is the set of pencils, and the universe is the set of objects. Assume that each region corresponds to a nonempty set.

How many subsets are there in a set with $p$ elements?

Let U=\{1,2,3,4,5,6,7,8,9,10\} A=\{2,3,5,6,7\} B=\{4,5,6,7,8\} List all the members of the set. $\bar { A }$