Question 1

Construct a truth table for the statement.
-$\sim \mathrm{s} \vee(\sim \mathrm{p} \vee \mathrm{s})$

Accepted Answer

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

Question 2

Label the pair of statements as either contrary or consistent.
-That old book is full of recipes. That book is very expensive.

Accepted Answer

A) Contrary 
B) Consistent 
A) Contrary 
B) Consistent B

Question 3

Decide whether the statement is compound.
-$\sqrt { 4 }$ is rational and $\sqrt { 6 }$ is irrational.

Accepted Answer

A)  Not compound 
B)  Compound 
A)  Not compound 
B)  Compound B

Question 4

Decide whether the statement is compound.
-If it rains, we won't play soccer.

Accepted Answer

A) Compound 
B) Not compound 
A) Compound 
B) Not compound

Question 5

Use a truth table to determine whether the argument is valid.
-$ p \vee q $
$ \frac{\sim(p \vee q)}{\sim q} $

Accepted Answer

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

Question 6

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$
-If she doesn't study, she won't pass her math test.

Accepted Answer

A) She doesn't study and will pass her math test. 
B) If she doesn't study, she will pass her math test. 
C) She studies and will pass her math test. 
D) She doesn't study and she won't pass her math test. 
A) She doesn't study and will pass her math test. 
B) If she doesn't study, she will pass her math test. 
C) She studies and will pass her math test. 
D) She doesn't study and she won't pass her math test.

Question 7

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-All chocolate is good.

Accepted Answer

A) If it's good, then it's got to be chocolate. 
B) Chocolate is good. 
C) If it isn't chocolate, then it isn't good. 
D) If it's chocolate, then it's good. 
A) If it's good, then it's got to be chocolate. 
B) Chocolate is good. 
C) If it isn't chocolate, then it isn't good. 
D) If it's chocolate, then it's good.

Question 8

Decide whether the statement is true or false.
-All whole numbers are real numbers.

Accepted Answer

A) True 
 B)False

Question 9

Tell whether the conditional statement is true or false.
-$( 52 \neq 25 ) \rightarrow ( 2 + 3 = 5 )$

Accepted Answer

A) True 
 B)False

Question 10

Use an Euler diagram to determine whether the argument is valid or invalid.
-Some cars are considered sporty.
$\underline { \text { Some cars are safe at high speeds. } }$
Some sports cars are safe at high speeds.

Accepted Answer

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

Question 11

Write a logical statement representing the following circuit. Simplify when possible.
-$[ ( p \wedge \sim r ) \vee q ] \wedge ( q \wedge \sim r )$

Accepted Answer

The statem

Question 12

The argument has a true conclusion. Identify the argument as valid or invalid.
-$\sqrt { 14 }$ is less than 14 .
$\underline { \text {7 is less than }\sqrt { 14 } }$
$\sqrt { 14 }$ is less than $7 .$

Accepted Answer

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

Question 13

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 the food won't be good and I won't eat too much.

Accepted Answer

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

Question 14

Label the pair of statements as either contrary or consistent.
-Today is Tuesday. Today it is raining.

Accepted Answer

A) Consistent 
B) Contrary 
A) Consistent 
B) Contrary

Question 15

Solve the problem.
-Given that $( p \vee q ) \vee \sim p$ is true, what can you conclude about the truth values of $p$ and $q$ ?

Accepted Answer

A)  $q$ is true 
B)  $p$ and $q$ can have any truth values 
C)  At least one of $p$ and $q$ is true 
D)  $p$ is true 
A)  $q$ is true 
B)  $p$ and $q$ can have any truth values 
C)  At least one of $p$ and $q$ is true 
D)  $p$ is true

Question 16

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$
-If you give your hat to the doorman, he will give you a dirty look.

Accepted Answer

A) If you give your hat to the doorman he will not give you a dirty look. 
B) You do not give your hat to the doorman and he will not give you a dirty look. 
C) You give your hat to the doorman and he will not give you a dirty look. 
D) You do not give your hat to the doorman and he will give you a dirty look. 
A) If you give your hat to the doorman he will not give you a dirty look. 
B) You do not give your hat to the doorman and he will not give you a dirty look. 
C) You give your hat to the doorman and he will not give you a dirty look. 
D) You do not give your hat to the doorman and he will give you a dirty look.

Question 17

Construct a truth table for the statement.
-$( \sim \mathrm { p } \vee \sim \mathrm { q } ) \rightarrow \sim ( \mathrm { q } \wedge \mathrm { p } )$

Accepted Answer

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

Question 18

Tell whether the conditional statement is true or false.
-Here T represents a true statement. $\mathrm { T } \rightarrow ( - 3 > - 5 )$

Accepted Answer

A) True 
 B)False

Question 19

Write the converse, inverse, or contrapositive of the statement as requested.
-All Border Collies are dogs. Inverse

Accepted Answer

A) If it's a Border Collie, it's not a dog 
B) If it's not a dog, it's not a Border Collie. 
C) If it's a dog, it's a Border Collie. 
D) If it's not a Border Collie, it's not a dog. 
A) If it's a Border Collie, it's not a dog 
B) If it's not a dog, it's not a Border Collie. 
C) If it's a dog, it's a Border Collie. 
D) If it's not a Border Collie, it's not a dog.

Question 20

Rewrite the statement in the form "if p, then q".
-I won't go until it's 11 pm.

Accepted Answer

A) If I don't go, then it's not 11 pm. 
B) If it's not 11 pm, then I won't go. 
C) If I go, then it's 11 pm. 
D) If it's 11 pm, then I'll go. 
A) If I don't go, then it's not 11 pm. 
B) If it's not 11 pm, then I won't go. 
C) If I go, then it's 11 pm. 
D) If it's 11 pm, then I'll go.

Construct a truth table for the statement. - $\sim \mathrm{s} \vee(\sim \mathrm{p} \vee \mathrm{s})$

Label the pair of statements as either contrary or consistent. -That old book is full of recipes. That book is very expensive.

Decide whether the statement is compound. - $\sqrt { 4 }$ is rational and $\sqrt { 6 }$ is irrational.

Decide whether the statement is compound. -If it rains, we won't play soccer.

Use a truth table to determine whether the argument is valid. - $p \vee q$ $\frac{\sim(p \vee q)}{\sim q}$

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$ -If she doesn't study, she won't pass her math test.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -All chocolate is good.

Decide whether the statement is true or false. -All whole numbers are real numbers.

Tell whether the conditional statement is true or false. - $( 52 \neq 25 ) \rightarrow ( 2 + 3 = 5 )$

Use an Euler diagram to determine whether the argument is valid or invalid. -Some cars are considered sporty. $\underline { \text { Some cars are safe at high speeds. } }$ Some sports cars are safe at high speeds.

Write a logical statement representing the following circuit. Simplify when possible. - $[ ( p \wedge \sim r ) \vee q ] \wedge ( q \wedge \sim r )$

The argument has a true conclusion. Identify the argument as valid or invalid. - $\sqrt { 14 }$ is less than 14 . $\underline { \text {7 is less than }\sqrt { 14 } }$ $\sqrt { 14 }$ is less than $7 .$

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 the food won't be good and I won't eat too much.

Label the pair of statements as either contrary or consistent. -Today is Tuesday. Today it is raining.

Solve the problem. -Given that $( p \vee q ) \vee \sim p$ is true, what can you conclude about the truth values of $p$ and $q$ ?

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$ -If you give your hat to the doorman, he will give you a dirty look.

Construct a truth table for the statement. - $( \sim \mathrm { p } \vee \sim \mathrm { q } ) \rightarrow \sim ( \mathrm { q } \wedge \mathrm { p } )$

Tell whether the conditional statement is true or false. -Here T represents a true statement. $\mathrm { T } \rightarrow ( - 3 > - 5 )$

Write the converse, inverse, or contrapositive of the statement as requested. -All Border Collies are dogs. Inverse

Rewrite the statement in the form "if p, then q". -I won't go until it's 11 pm.

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

Construct a truth table for the statement. - ∼s∨(∼p∨s)\sim \mathrm{s} \vee(\sim \mathrm{p} \vee \mathrm{s})∼s∨(∼p∨s)

Label the pair of statements as either contrary or consistent. -That old book is full of recipes. That book is very expensive.

Decide whether the statement is compound. - 4\sqrt { 4 }4​ is rational and 6\sqrt { 6 }6​ is irrational.

Decide whether the statement is compound. -If it rains, we won't play soccer.

Use a truth table to determine whether the argument is valid. - p∨q p \vee q p∨q ∼(p∨q)∼q \frac{\sim(p \vee q)}{\sim q} ∼q∼(p∨q)​

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -All chocolate is good.

Decide whether the statement is true or false. -All whole numbers are real numbers.

Tell whether the conditional statement is true or false. - (52≠25)→(2+3=5)( 52 \neq 25 ) \rightarrow ( 2 + 3 = 5 )(52=25)→(2+3=5)

Use an Euler diagram to determine whether the argument is valid or invalid. -Some cars are considered sporty. Some cars are safe at high speeds. ‾\underline { \text { Some cars are safe at high speeds. } } Some cars are safe at high speeds. ​ Some sports cars are safe at high speeds.

Write a logical statement representing the following circuit. Simplify when possible. - [(p∧∼r)∨q]∧(q∧∼r)[ ( p \wedge \sim r ) \vee q ] \wedge ( q \wedge \sim r )[(p∧∼r)∨q]∧(q∧∼r)

The argument has a true conclusion. Identify the argument as valid or invalid. - 14\sqrt { 14 }14​ is less than 14 . 7 is less than 14‾\underline { \text {7 is less than }\sqrt { 14 } }7 is less than 14​​ 14\sqrt { 14 }14​ is less than 7.7 .7.

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 the food won't be good and I won't eat too much.

Label the pair of statements as either contrary or consistent. -Today is Tuesday. Today it is raining.

Solve the problem. -Given that (p∨q)∨∼p( p \vee q ) \vee \sim p(p∨q)∨∼p is true, what can you conclude about the truth values of ppp and qqq ?

Construct a truth table for the statement. - (∼p∨∼q)→∼(q∧p)( \sim \mathrm { p } \vee \sim \mathrm { q } ) \rightarrow \sim ( \mathrm { q } \wedge \mathrm { p } )(∼p∨∼q)→∼(q∧p)

Tell whether the conditional statement is true or false. -Here T represents a true statement. T→(−3>−5)\mathrm { T } \rightarrow ( - 3 > - 5 )T→(−3>−5)

Write the converse, inverse, or contrapositive of the statement as requested. -All Border Collies are dogs. Inverse

Rewrite the statement in the form "if p, then q". -I won't go until it's 11 pm.

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

Construct a truth table for the statement. - $\sim \mathrm{s} \vee(\sim \mathrm{p} \vee \mathrm{s})$

Decide whether the statement is compound. - $\sqrt { 4 }$ is rational and $\sqrt { 6 }$ is irrational.

Use a truth table to determine whether the argument is valid. - $p \vee q$ $\frac{\sim(p \vee q)}{\sim q}$

Tell whether the conditional statement is true or false. - $( 52 \neq 25 ) \rightarrow ( 2 + 3 = 5 )$

Use an Euler diagram to determine whether the argument is valid or invalid. -Some cars are considered sporty. $\underline { \text { Some cars are safe at high speeds. } }$ Some sports cars are safe at high speeds.

Write a logical statement representing the following circuit. Simplify when possible. - $[ ( p \wedge \sim r ) \vee q ] \wedge ( q \wedge \sim r )$

The argument has a true conclusion. Identify the argument as valid or invalid. - $\sqrt { 14 }$ is less than 14 . $\underline { \text {7 is less than }\sqrt { 14 } }$ $\sqrt { 14 }$ is less than $7 .$

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 the food won't be good and I won't eat too much.

Solve the problem. -Given that $( p \vee q ) \vee \sim p$ is true, what can you conclude about the truth values of $p$ and $q$ ?

Construct a truth table for the statement. - $( \sim \mathrm { p } \vee \sim \mathrm { q } ) \rightarrow \sim ( \mathrm { q } \wedge \mathrm { p } )$

Tell whether the conditional statement is true or false. -Here T represents a true statement. $\mathrm { T } \rightarrow ( - 3 > - 5 )$