Question 1

Determine whether the statements are logically equivalent.
-$\mathrm { q } \rightarrow \mathrm { p }$ and $\sim \mathrm { q } \vee \mathrm { p }$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 2

Determine whether the statements are logically equivalent.
-$\sim \mathrm { q } \wedge \mathrm { p }$ and $\sim \mathrm { q } \rightarrow \mathrm { p }$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 3

$$\text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. }$$
-$3 _{-} \{ 1,2,3 , \ldots , 10 \}$

Accepted Answer

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

Question 4

Determine whether the following is a statement. If it is, then also classify the statement as true or false.
-The state of California is in North America.

Accepted Answer

A) Not a statement 
B) True statement 
C) False statement 
A) Not a statement 
B) True statement 
C) False statement

Question 5

Write a statement that represents the relationship between the following.
-$\varnothing$ and $B = \{ a , b , c , d , e \}$

Accepted Answer

A)  $\varnothing \not \subset B$ 
B)  $\varnothing = B$ 
C)  $\varnothing \in B$ 
D)  $\varnothing \subset B$ 
A)  $\varnothing \not \subset B$ 
B)  $\varnothing = B$ 
C)  $\varnothing \in B$ 
D)  $\varnothing \subset B$

Question 6

$$\text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. }$$
-$\{ 3 \} _{-} \{ 1,2,3 , \ldots , 10 \}$

Accepted Answer

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

Question 7

Write in if-then form.
-Practice is necessary for making the team.

Accepted Answer

A) If you don't practice, then you won't make the team. 
B) If you practice, then you will make the team. 
C) If you make the team, then you won't have to practice. 
D) If you make the team, then you must practice. 
A) If you don't practice, then you won't make the team. 
B) If you practice, then you will make the team. 
C) If you make the team, then you won't have to practice. 
D) If you make the team, then you must practice.

Question 8

Write a valid conclusion based on the statements.
-Smiling people are happy. Alert people are not happy. Careful drivers are alert. Careless drivers have accidents.

Accepted Answer

A) Careful drivers are happy. 
B) People who smile are alert. 
C) Careful drivers have accidents. 
D) People who smile have accidents. 
A) Careful drivers are happy. 
B) People who smile are alert. 
C) Careful drivers have accidents. 
D) People who smile have accidents.

Question 9

Provide an appropriate response.
-Translate into symbolic form the following statement and explain: If it is not warm and
sunny, then we cannot go to the beach.

Accepted Answer

The answer of Provide an appropriate response.
-Translate into symbolic form...

Question 10

Write the statement indicated.
-State the inverse of the following: If you practice, then you will win.

Accepted Answer

A) If you practice, then you will not win. 
B) If you do not win, then you did not practice. 
C) If you win, then you practiced. 
D) If you do not practice, then you will not win. 
A) If you practice, then you will not win. 
B) If you do not win, then you did not practice. 
C) If you win, then you practiced. 
D) If you do not practice, then you will not win.

Question 11

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in symbolic form.
-If the food is not good, I won't eat too much.

Accepted Answer

A)  $\sim p \rightarrow \sim r$ 
B)  $\sim ( \mathrm { r } - \mathrm { p } )$ 
C)  $\sim r \rightarrow \sim p$ 
D)  $\mathrm { r } \rightarrow \sim \mathrm { p }$ 
A)  $\sim p \rightarrow \sim r$ 
B)  $\sim ( \mathrm { r } - \mathrm { p } )$ 
C)  $\sim r \rightarrow \sim p$ 
D)  $\mathrm { r } \rightarrow \sim \mathrm { p }$

Question 12

Determine whether the following is a statement. If it is, then also classify the statement as true or false.
-5 - 1 = 4

Accepted Answer

A) True statement 
B) Not a statement 
C) False statement 
A) True statement 
B) Not a statement 
C) False statement

Question 13

Find n(A)for the set A.
-$A = \{ x \mid x \in N$ and $17 \leq x \leq 25 \}$

Accepted Answer

A)  9 
B)  42 
C)  43 
D)  7 
A)  9 
B)  42 
C)  43 
D)  7

Question 14

Construct a truth table for the statement.
-$(p \wedge w) \wedge(\sim w \vee t)$

Accepted Answer

A) 
$\begin{array}{cccc}
\mathrm{p} & \mathrm{w} & \mathrm{t} & (\mathrm{p} \wedge \mathrm{W}) \wedge(\sim \mathrm{W} \vee \mathrm{t}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$ 
B) 
$\begin{array}{cccc}
\mathrm{p} & \mathrm{w} & \mathrm{t} & (\mathrm{p} \wedge \mathrm{w}) \wedge(\sim \mathrm{w} \vee \mathrm{t}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
A) 
$\begin{array}{cccc}
\mathrm{p} & \mathrm{w} & \mathrm{t} & (\mathrm{p} \wedge \mathrm{W}) \wedge(\sim \mathrm{W} \vee \mathrm{t}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$ 
B) 
$\begin{array}{cccc}
\mathrm{p} & \mathrm{w} & \mathrm{t} & (\mathrm{p} \wedge \mathrm{w}) \wedge(\sim \mathrm{w} \vee \mathrm{t}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$

Question 15

Determine whether the statements are logically equivalent.
-$\sim \mathrm { p } \wedge \sim \mathrm { q }$ and $\sim ( \mathrm { p } \vee \mathrm { q } )$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 16

Restate in a logically equivalent form.
-It is not true that today I both went to school and read a book.

Accepted Answer

A) Today, I did not read a book and did not go to school. 
B) Today, I read a book but did not go to school. 
C) Today, I either did not go to school or I did not read a book. 
D) Today, I went to school and read a book. 
A) Today, I did not read a book and did not go to school. 
B) Today, I read a book but did not go to school. 
C) Today, I either did not go to school or I did not read a book. 
D) Today, I went to school and read a book.

Question 17

Restate in a logically equivalent form.
-If a number is divisible by 4 , then it is divisible by 2 .

Accepted Answer

A)  If a number is not divisible by 4 , then it is not divisible by $2 .$ 
B)  If a number is not divisible by 2 , then it is not divisible by 4 . 
C)  If a number is divisible by 4 , then it is not divisible by $2 .$ 
D)  If a number is not divisible by 4 , then it is divisible by $2 .$ 
A)  If a number is not divisible by 4 , then it is not divisible by $2 .$ 
B)  If a number is not divisible by 2 , then it is not divisible by 4 . 
C)  If a number is divisible by 4 , then it is not divisible by $2 .$ 
D)  If a number is not divisible by 4 , then it is divisible by $2 .$

Question 18

Write a statement that represents the relationship between the following.
-$A = \{ a , e , i , o , u \}$ and $B = \{ e , o , i , u , a \}$

Accepted Answer

A)  $A \subset B$ 
B)  e $\subseteq B$ 
C)  $a = \mathrm { A }$ 
D)  $A = B$ 
A)  $A \subset B$ 
B)  e $\subseteq B$ 
C)  $a = \mathrm { A }$ 
D)  $A = B$

Question 19

Write a valid conclusion based on the statements.
-All fish can dream. Any dead animal is unable to dream. All live animals have a heartbeat.

Accepted Answer

A) Any dead animal has no heartbeat. 
B) All fish have a heartbeat. 
C) Any dead fish can dream. 
D) All live animals can dream. 
A) Any dead animal has no heartbeat. 
B) All fish have a heartbeat. 
C) Any dead fish can dream. 
D) All live animals can dream.

Question 20

Do the following represent equal sets?
-{p, q, r, s} = {q, s, r, p}

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Determine whether the statements are logically equivalent. - $\mathrm { q } \rightarrow \mathrm { p }$ and $\sim \mathrm { q } \vee \mathrm { p }$

Determine whether the statements are logically equivalent. - $\sim \mathrm { q } \wedge \mathrm { p }$ and $\sim \mathrm { q } \rightarrow \mathrm { p }$

$\text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. }$ - $3 _{-} \{ 1,2,3 , \ldots , 10 \}$

Determine whether the following is a statement. If it is, then also classify the statement as true or false. -The state of California is in North America.

Write a statement that represents the relationship between the following. - $\varnothing$ and $B = \{ a , b , c , d , e \}$

$\text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. }$ - $\{ 3 \} _{-} \{ 1,2,3 , \ldots , 10 \}$

Write in if-then form. -Practice is necessary for making the team.

Write a valid conclusion based on the statements. -Smiling people are happy. Alert people are not happy. Careful drivers are alert. Careless drivers have accidents.

Provide an appropriate response. -Translate into symbolic form the following statement and explain: If it is not warm and sunny, then we cannot go to the beach.

Write the statement indicated. -State the inverse of the following: If you practice, then you will win.

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in symbolic form. -If the food is not good, I won't eat too much.

Determine whether the following is a statement. If it is, then also classify the statement as true or false. -5 - 1 = 4

Find n(A)for the set A. - $A = \{ x \mid x \in N$ and $17 \leq x \leq 25 \}$

Construct a truth table for the statement. - $(p \wedge w) \wedge(\sim w \vee t)$

Determine whether the statements are logically equivalent. - $\sim \mathrm { p } \wedge \sim \mathrm { q }$ and $\sim ( \mathrm { p } \vee \mathrm { q } )$

Restate in a logically equivalent form. -It is not true that today I both went to school and read a book.

Restate in a logically equivalent form. -If a number is divisible by 4 , then it is divisible by 2 .

Write a statement that represents the relationship between the following. - $A = \{ a , e , i , o , u \}$ and $B = \{ e , o , i , u , a \}$

Write a valid conclusion based on the statements. -All fish can dream. Any dead animal is unable to dream. All live animals have a heartbeat.

Do the following represent equal sets? -{p, q, r, s} = {q, s, r, p}

An Introduction to Problem Solving

Numeration Systems and Whole Number Operations

Number Theory

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

Exam 2: Introduction to Logic and Sets

Determine whether the statements are logically equivalent. - q→p\mathrm { q } \rightarrow \mathrm { p }q→p and ∼q∨p\sim \mathrm { q } \vee \mathrm { p }∼q∨p

Determine whether the statements are logically equivalent. - ∼q∧p\sim \mathrm { q } \wedge \mathrm { p }∼q∧p and ∼q→p\sim \mathrm { q } \rightarrow \mathrm { p }∼q→p

Indicate which symbol, ∈ or ∉ makes the statement true. \text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. } Indicate which symbol, ∈ or ∈/ makes the statement true. - 3−{1,2,3,…,10}3 _{-} \{ 1,2,3 , \ldots , 10 \}3−​{1,2,3,…,10}

Determine whether the following is a statement. If it is, then also classify the statement as true or false. -The state of California is in North America.

Write a statement that represents the relationship between the following. - ∅\varnothing∅ and B={a,b,c,d,e}B = \{ a , b , c , d , e \}B={a,b,c,d,e}

Indicate which symbol, ∈ or ∉ makes the statement true. \text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. } Indicate which symbol, ∈ or ∈/ makes the statement true. - {3}−{1,2,3,…,10}\{ 3 \} _{-} \{ 1,2,3 , \ldots , 10 \}{3}−​{1,2,3,…,10}

Write in if-then form. -Practice is necessary for making the team.

Write a valid conclusion based on the statements. -Smiling people are happy. Alert people are not happy. Careful drivers are alert. Careless drivers have accidents.

Provide an appropriate response. -Translate into symbolic form the following statement and explain: If it is not warm and sunny, then we cannot go to the beach.

Write the statement indicated. -State the inverse of the following: If you practice, then you will win.

Letting r stand for "The food is good," p stand for "I eat too much," and q stand for "I'll exercise," write the following in symbolic form. -If the food is not good, I won't eat too much.

Determine whether the following is a statement. If it is, then also classify the statement as true or false. -5 - 1 = 4

Find n(A)for the set A. - A={x∣x∈NA = \{ x \mid x \in NA={x∣x∈N and 17≤x≤25}17 \leq x \leq 25 \}17≤x≤25}

Construct a truth table for the statement. - (p∧w)∧(∼w∨t)(p \wedge w) \wedge(\sim w \vee t)(p∧w)∧(∼w∨t)

Determine whether the statements are logically equivalent. - ∼p∧∼q\sim \mathrm { p } \wedge \sim \mathrm { q }∼p∧∼q and ∼(p∨q)\sim ( \mathrm { p } \vee \mathrm { q } )∼(p∨q)

Restate in a logically equivalent form. -It is not true that today I both went to school and read a book.

Restate in a logically equivalent form. -If a number is divisible by 4 , then it is divisible by 2 .

Write a statement that represents the relationship between the following. - A={a,e,i,o,u}A = \{ a , e , i , o , u \}A={a,e,i,o,u} and B={e,o,i,u,a}B = \{ e , o , i , u , a \}B={e,o,i,u,a}

Write a valid conclusion based on the statements. -All fish can dream. Any dead animal is unable to dream. All live animals have a heartbeat.

Do the following represent equal sets? -{p, q, r, s} = {q, s, r, p}

An Introduction to Problem Solving

Numeration Systems and Whole Number Operations

Number Theory

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Constructions

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

Determine whether the statements are logically equivalent. - $\mathrm { q } \rightarrow \mathrm { p }$ and $\sim \mathrm { q } \vee \mathrm { p }$

Determine whether the statements are logically equivalent. - $\sim \mathrm { q } \wedge \mathrm { p }$ and $\sim \mathrm { q } \rightarrow \mathrm { p }$

$\text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. }$ - $3 _{-} \{ 1,2,3 , \ldots , 10 \}$

Write a statement that represents the relationship between the following. - $\varnothing$ and $B = \{ a , b , c , d , e \}$

$\text { Indicate which symbol, } \in \text { or } \notin \text { makes the statement true. }$ - $\{ 3 \} _{-} \{ 1,2,3 , \ldots , 10 \}$

Find n(A)for the set A. - $A = \{ x \mid x \in N$ and $17 \leq x \leq 25 \}$

Construct a truth table for the statement. - $(p \wedge w) \wedge(\sim w \vee t)$

Determine whether the statements are logically equivalent. - $\sim \mathrm { p } \wedge \sim \mathrm { q }$ and $\sim ( \mathrm { p } \vee \mathrm { q } )$

Write a statement that represents the relationship between the following. - $A = \{ a , e , i , o , u \}$ and $B = \{ e , o , i , u , a \}$