Question 1

Use a truth table to determine whether the argument is valid.
-

Accepted Answer

A)  Valid 
B)  Invalid 
A)  Valid 
B)  Invalid

Question 2

Given p is true, q is true, and r is false, find the truth value of the statement.
-$[ ( \sim p \rightarrow r ) \wedge ( \sim p \vee q ) ] \rightarrow r$

Accepted Answer

A) True 
 B)False

Question 3

$$\text { Let } p \text { represent } 7 < 8 \text {, } q \text { represent } 2 < 5 < 6 \text {, and } \mathbf { r } \text { represent } 3 < 2 \text {. Decide whether the statement is true or false. }$$
-$( \sim \mathrm { r } \wedge \sim \mathrm { q } ) \vee ( \sim \mathrm { r } \wedge \mathrm { q } )$

Accepted Answer

A) True 
 B)False

Question 4

Write the compound statement in symbols. Let $r =$ "The food is good."
$\begin{array} { l } 
p = \text { "I eat too much." } \
q = \text { "I'll exercise." }
\end{array}$
-If I exercise, then I won't eat too much.

Accepted Answer

A)  $q \rightarrow \sim p$ 
B)  $\sim ( p \rightarrow q )$ 
C)  $p \rightarrow q$ 
D)  $r \wedge p$ 
A)  $q \rightarrow \sim p$ 
B)  $\sim ( p \rightarrow q )$ 
C)  $p \rightarrow q$ 
D)  $r \wedge p$

Question 5

Decide whether the statement is true or false.
-There exists a rational number that is an integer.

Accepted Answer

A) True 
 B)False

Question 6

Give the number of rows in the truth table for the compound statement.
-$( p \vee q ) \vee ( \sim r \wedge s ) \vee \sim t$

Accepted Answer

A) 10 
B) 32 
C) 8 
D) 25 
A) 10 
B) 32 
C) 8 
D) 25

Question 7

Find the truth value of the statement.
-$10 + 1 = 7 \text { if and only if } 12 = 14$

Accepted Answer

A) True 
 B)False

Question 8

Write an equivalent statement that does not use the if ... then connec $\text { Use the fact that } p \rightarrow q \text { is equivalent to } \sim p \vee q \text {. }$
-If Rita does not want to go, then she stays home.

Accepted Answer

A) Rita does want to go or she does not stay home. 
B) Rita does want to go or she stays home. 
C) Rita does not want to go so she stays home. 
D) Rita does not want to go and she does not stay home. 
A) Rita does want to go or she does not stay home. 
B) Rita does want to go or she stays home. 
C) Rita does not want to go so she stays home. 
D) Rita does not want to go and she does not stay home.

Question 9

Construct a truth table for the statement.
-$\sim \mathrm{r} \wedge \sim \mathrm{p}$

Accepted Answer

A) 
$\begin{array}{ccc}
\mathrm{r} & \mathrm{p} & (\sim \mathrm{r} \wedge \sim \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
B) 
$\begin{array}{ccc}
\mathrm{r} & \mathrm{p} & (\sim \mathrm{r} \wedge \sim \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
C) 
$\begin{array}{ccc}
\mathrm{r} & \mathrm{p} & (\sim \mathrm{r} \wedge \sim \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$ 
D) 
$\begin{array}{ccc}
\mathrm{r} & \mathrm{p} & (\sim \mathrm{r} \wedge \sim \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
A) 
$\begin{array}{ccc}
\mathrm{r} & \mathrm{p} & (\sim \mathrm{r} \wedge \sim \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
B) 
$\begin{array}{ccc}
\mathrm{r} & \mathrm{p} & (\sim \mathrm{r} \wedge \sim \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
C) 
$\begin{array}{ccc}
\mathrm{r} & \mathrm{p} & (\sim \mathrm{r} \wedge \sim \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$ 
D) 
$\begin{array}{ccc}
\mathrm{r} & \mathrm{p} & (\sim \mathrm{r} \wedge \sim \mathrm{p}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$

Question 10

Determine if the argument is valid or a fallacy. Give a reason to justify answer.
-If you read, then you will have a high score.
$\underline { \text {You do not read.} }$
You will not have a high score.

Accepted Answer

A)  Fallacy by fallacy of the converse 
B)  Valid by reasoning of transitivity 
C)  Fallacy by fallacy of the inverse 
D)  Valid by modus tollens 
A)  Fallacy by fallacy of the converse 
B)  Valid by reasoning of transitivity 
C)  Fallacy by fallacy of the inverse 
D)  Valid by modus tollens

Question 11

Decide whether the statement is true or false.
-$\text { For no real number } y , | y |  0 \text {. }$

Accepted Answer

A) True 
 B)False

Question 12

Decide whether or not the following is a statement.
-My favorite baseball team will win the pennant.

Accepted Answer

A) Not a statement 
B) Statement 
A) Not a statement 
B) Statement

Question 13

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$
-If it is raining, you take your coat.

Accepted Answer

A) It is not raining and you take your coat. 
B) If it is raining, you do not take your coat. 
C) It is raining and you do not take your coat. 
D) It is not raining and you do not take your coat. 
A) It is not raining and you take your coat. 
B) If it is raining, you do not take your coat. 
C) It is raining and you do not take your coat. 
D) It is not raining and you do not take your coat.

Question 14

Determine if the argument is valid or a fallacy. Give a reason to justify answer.
-If the bough breaks, then the cradle will fall.
$\underline { \text {The bough breaks.} }$
The cradle will fall.

Accepted Answer

A)  Valid by reasoning of transitivity 
B)  Fallacy by fallacy of the inverse 
C)  Fallacy by fallacy of the converse 
D)  Valid by modus ponens 
A)  Valid by reasoning of transitivity 
B)  Fallacy by fallacy of the inverse 
C)  Fallacy by fallacy of the converse 
D)  Valid by modus ponens

Question 15

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols.
-Jim plays football and Michael plays basketball.

Accepted Answer

A)  $\sim p \wedge q$ 
B)  $p \vee q$ 
C)  $\mathrm { p } \wedge \mathrm { q }$ 
D)  $\mathrm { p } \mathrm {} \vee \sim \mathrm { q }$ 
A)  $\sim p \wedge q$ 
B)  $p \vee q$ 
C)  $\mathrm { p } \wedge \mathrm { q }$ 
D)  $\mathrm { p } \mathrm {} \vee \sim \mathrm { q }$

Use a truth table to determine whether the argument is valid. -

Given p is true, q is true, and r is false, find the truth value of the statement. - $[ ( \sim p \rightarrow r ) \wedge ( \sim p \vee q ) ] \rightarrow r$

Write the compound statement in symbols. Let $r =$ "The food is good." p= "I eat too much." q= "I'll exercise." -If I exercise, then I won't eat too much.

Decide whether the statement is true or false. -There exists a rational number that is an integer.

Give the number of rows in the truth table for the compound statement. - $( p \vee q ) \vee ( \sim r \wedge s ) \vee \sim t$

Find the truth value of the statement. - $10 + 1 = 7 \text { if and only if } 12 = 14$

Write an equivalent statement that does not use the if ... then connec $\text { Use the fact that } p \rightarrow q \text { is equivalent to } \sim p \vee q \text {. }$ -If Rita does not want to go, then she stays home.

Construct a truth table for the statement. - $\sim \mathrm{r} \wedge \sim \mathrm{p}$

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If you read, then you will have a high score. $\underline { \text {You do not read.} }$ You will not have a high score.

Decide whether the statement is true or false. - $\text { For no real number } y , | y | < 0 \text { and } y ^ { 3 } > 0 \text {. }$

Decide whether or not the following is a statement. -My favorite baseball team will win the pennant.

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$ -If it is raining, you take your coat.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If the bough breaks, then the cradle will fall. $\underline { \text {The bough breaks.} }$ The cradle will fall.

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -Jim plays football and Michael plays basketball.

The Art of Problem Solving

The Basic Concepts of Set Theory

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 3: Introduction to Logic

Use a truth table to determine whether the argument is valid. -

Given p is true, q is true, and r is false, find the truth value of the statement. - [(∼p→r)∧(∼p∨q)]→r[ ( \sim p \rightarrow r ) \wedge ( \sim p \vee q ) ] \rightarrow r[(∼p→r)∧(∼p∨q)]→r

Write the compound statement in symbols. Let r=r =r= "The food is good." p= "I eat too much." q= "I'll exercise." -If I exercise, then I won't eat too much.

Decide whether the statement is true or false. -There exists a rational number that is an integer.

Give the number of rows in the truth table for the compound statement. - (p∨q)∨(∼r∧s)∨∼t( p \vee q ) \vee ( \sim r \wedge s ) \vee \sim t(p∨q)∨(∼r∧s)∨∼t

Find the truth value of the statement. - 10+1=7 if and only if 12=1410 + 1 = 7 \text { if and only if } 12 = 1410+1=7 if and only if 12=14

Construct a truth table for the statement. - ∼r∧∼p\sim \mathrm{r} \wedge \sim \mathrm{p}∼r∧∼p

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If you read, then you will have a high score. You do not read.‾\underline { \text {You do not read.} }You do not read.​ You will not have a high score.

Decide whether the statement is true or false. - For no real number y,∣y∣<0 and y3>0. \text { For no real number } y , | y | < 0 \text { and } y ^ { 3 } > 0 \text {. } For no real number y,∣y∣<0 and y3>0.

Decide whether or not the following is a statement. -My favorite baseball team will win the pennant.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If the bough breaks, then the cradle will fall. The bough breaks.‾\underline { \text {The bough breaks.} }The bough breaks.​ The cradle will fall.

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -Jim plays football and Michael plays basketball.

The Art of Problem Solving

The Basic Concepts of Set Theory

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

Given p is true, q is true, and r is false, find the truth value of the statement. - $[ ( \sim p \rightarrow r ) \wedge ( \sim p \vee q ) ] \rightarrow r$

Write the compound statement in symbols. Let $r =$ "The food is good." p= "I eat too much." q= "I'll exercise." -If I exercise, then I won't eat too much.

Give the number of rows in the truth table for the compound statement. - $( p \vee q ) \vee ( \sim r \wedge s ) \vee \sim t$

Find the truth value of the statement. - $10 + 1 = 7 \text { if and only if } 12 = 14$

Construct a truth table for the statement. - $\sim \mathrm{r} \wedge \sim \mathrm{p}$

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If you read, then you will have a high score. $\underline { \text {You do not read.} }$ You will not have a high score.

Decide whether the statement is true or false. - $\text { For no real number } y , | y | < 0 \text { and } y ^ { 3 } > 0 \text {. }$

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If the bough breaks, then the cradle will fall. $\underline { \text {The bough breaks.} }$ The cradle will fall.