Question 1

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-No turkeys like Thanksgiving.

Accepted Answer

A) If it is a turkey, then it doesn't like Thanksgiving. 
B) If it is not a turkey, then it likes Thanksgiving. 
C) If it is Thanksgiving, then turkeys like it. 
D) If it is not Thanksgiving, then no turkeys like it. 
A) If it is a turkey, then it doesn't like Thanksgiving. 
B) If it is not a turkey, then it likes Thanksgiving. 
C) If it is Thanksgiving, then turkeys like it. 
D) If it is not Thanksgiving, then no turkeys like it.

Question 2

Use De Morgan's laws to write the negation of the statement.
-Denim is out and linen is in.

Accepted Answer

A) Denim is not out and linen is out. 
B) Denim and linen are in. 
C) Denim is in and linen is out. 
D) Denim is not out or linen is not in. 
A) Denim is not out and linen is out. 
B) Denim and linen are in. 
C) Denim is in and linen is out. 
D) Denim is not out or linen is not in.

Question 3

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement.
-$\sim ( p \wedge q ) \wedge ( r \vee \sim q )$

Accepted Answer

A) True 
 B)False

Question 4

Label the pair of statements as either contrary or consistent.
-That car is missing 3 tires. That car is in perfect condition.

Accepted Answer

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

Question 5

Decide whether or not the following is a statement.
-Go fly a kite.

Accepted Answer

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

Question 6

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-I'll leave when he arrives.

Accepted Answer

A) If I leave, then he will leave. 
B) If I will leave, then he'll arrive. 
C) I'll leave when he arrives. 
D) If he arrives, then I'll leave. 
A) If I leave, then he will leave. 
B) If I will leave, then he'll arrive. 
C) I'll leave when he arrives. 
D) If he arrives, then I'll leave.

Question 7

If a conditional statement is true, its consequent must be true.

Accepted Answer

A) True 
 B)False

Question 8

Determine if the argument is valid or a fallacy. Give a reason to justify answer.
-If the bell rings, then we answer the door.
$\underline { \text {The bell rings.} }$
We answer the door.

Accepted Answer

A)  Fallacy by fallacy of the converse 
B)  Valid by modus ponens 
C)  Fallacy by fallacy of the inverse 
D)  Valid by disjunctive syllogism 
A)  Fallacy by fallacy of the converse 
B)  Valid by modus ponens 
C)  Fallacy by fallacy of the inverse 
D)  Valid by disjunctive syllogism

Question 9

Determine if the argument is valid or a fallacy. Give a reason to justify answer.
-If I'm hungry, then I will eat.
$\underline { \text {I'm not hungry.} }$
I will not eat.

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

When using a truth table, the statement $\sim \mathrm { p } \wedge \sim \mathrm { q }$ is equivalent to $\sim ( \mathrm { p } \vee \mathrm { q } )$.

Accepted Answer

A) True 
 B)False

Question 12

Solve the problem.
-Given that $\mathrm { p } \wedge \mathrm { q }$ is true, what can you conclude about the truth values of $\mathrm { p }$ and $\mathrm { q }$ ?

Accepted Answer

A)  Exactly one of $\mathrm { p }$ and $\mathrm { q }$ is true 
B)  Both $p$ and $q$ are true 
C)  At least one of $p$ and $q$ must be true 
D)  $\mathrm { p }$ and $\mathrm { q }$ have the same truth value 
A)  Exactly one of $\mathrm { p }$ and $\mathrm { q }$ is true 
B)  Both $p$ and $q$ are true 
C)  At least one of $p$ and $q$ must be true 
D)  $\mathrm { p }$ and $\mathrm { q }$ have the same truth value

Question 13

When using a truth table, the statement $q \wedge \sim p$ is equivalent to $\sim p \rightarrow \sim q$.

Accepted Answer

A) True 
 B)False

Question 14

Decide whether the statement is true or false.
-$\text { For every real number } x , x  5 \text {. }$

Accepted Answer

A) True 
 B)False

Question 15

Decide whether the statement is compound.
-Today is not Thursday.

Accepted Answer

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

Question 16

Decide whether or not the following is a statement.
-July 4 was a Monday.

Accepted Answer

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

Question 17

$$\text { When using a truth table, the statement } \sim q \wedge p \text { is equivalent to } \sim q \rightarrow p \text {. }$$

Accepted Answer

A) True 
 B)False

Question 18

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-Cats chase mice.

Accepted Answer

A)  Cats chase mice. 
B)  If a cat is chasing it, then it is a mouse. 
C)  If it is a cat, then it chases mice. 
D)  If cats chase, then they chase mice. 
A)  Cats chase mice. 
B)  If a cat is chasing it, then it is a mouse. 
C)  If it is a cat, then it chases mice. 
D)  If cats chase, then they chase mice.

Question 19

Determine if the argument is valid or a fallacy. Give a reason to justify answer.
-If you wear a tie, then you look natty.
$\underline { \text {You do not look natty.} }$
You are not wearing a tie.

Accepted Answer

A)  Fallacy by fallacy of the inverse 
B)  Valid by modus tollens 
C)  Fallacy by fallacy of the converse 
D)  Valid by disjunctive syllogism 
A)  Fallacy by fallacy of the inverse 
B)  Valid by modus tollens 
C)  Fallacy by fallacy of the converse 
D)  Valid by disjunctive syllogism

Question 20

Construct a truth table for the statement.
-$(\sim p \rightarrow q) \rightarrow(q \rightarrow \sim r)$

Accepted Answer

A) 
$\begin{array}{cccc}
\mathrm{p} & \mathrm{q} & \mathrm{r} & (\sim \mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\mathrm{q} \rightarrow \sim \mathrm{r}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$ 
B) 
$\begin{array}{cccc}
\mathrm{p} & \mathrm{q} & \mathrm{r} & (\sim \mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\mathrm{q} \rightarrow \sim \mathrm{r}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
C) 
  
D) 
  
A) 
$\begin{array}{cccc}
\mathrm{p} & \mathrm{q} & \mathrm{r} & (\sim \mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\mathrm{q} \rightarrow \sim \mathrm{r}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$ 
B) 
$\begin{array}{cccc}
\mathrm{p} & \mathrm{q} & \mathrm{r} & (\sim \mathrm{p} \rightarrow \mathrm{q}) \leftrightarrow(\mathrm{q} \rightarrow \sim \mathrm{r}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
C) 
  
D)

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -No turkeys like Thanksgiving.

Use De Morgan's laws to write the negation of the statement. -Denim is out and linen is in.

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - $\sim ( p \wedge q ) \wedge ( r \vee \sim q )$

Label the pair of statements as either contrary or consistent. -That car is missing 3 tires. That car is in perfect condition.

Decide whether or not the following is a statement. -Go fly a kite.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -I'll leave when he arrives.

If a conditional statement is true, its consequent must be true.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If the bell rings, then we answer the door. $\underline { \text {The bell rings.} }$ We answer the door.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If I'm hungry, then I will eat. $\underline { \text {I'm not hungry.} }$ I will not eat.

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

When using a truth table, the statement $\sim \mathrm { p } \wedge \sim \mathrm { q }$ is equivalent to $\sim ( \mathrm { p } \vee \mathrm { q } )$ .

Solve the problem. -Given that $\mathrm { p } \wedge \mathrm { q }$ is true, what can you conclude about the truth values of $\mathrm { p }$ and $\mathrm { q }$ ?

When using a truth table, the statement $q \wedge \sim p$ is equivalent to $\sim p \rightarrow \sim q$ .

Decide whether the statement is true or false. - $\text { For every real number } x , x < 6 \text { and } x > 5 \text {. }$

Decide whether the statement is compound. -Today is not Thursday.

Decide whether or not the following is a statement. -July 4 was a Monday.

$\text { When using a truth table, the statement } \sim q \wedge p \text { is equivalent to } \sim q \rightarrow p \text {. }$

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -Cats chase mice.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If you wear a tie, then you look natty. $\underline { \text {You do not look natty.} }$ You are not wearing a tie.

Construct a truth table for the statement. - $(\sim p \rightarrow q) \rightarrow(q \rightarrow \sim r)$

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

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -No turkeys like Thanksgiving.

Use De Morgan's laws to write the negation of the statement. -Denim is out and linen is in.

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - ∼(p∧q)∧(r∨∼q)\sim ( p \wedge q ) \wedge ( r \vee \sim q )∼(p∧q)∧(r∨∼q)

Label the pair of statements as either contrary or consistent. -That car is missing 3 tires. That car is in perfect condition.

Decide whether or not the following is a statement. -Go fly a kite.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -I'll leave when he arrives.

If a conditional statement is true, its consequent must be true.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If the bell rings, then we answer the door. The bell rings.‾\underline { \text {The bell rings.} }The bell rings.​ We answer the door.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If I'm hungry, then I will eat. I’m not hungry.‾\underline { \text {I'm not hungry.} }I’m not hungry.​ I will not eat.

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

When using a truth table, the statement ∼p∧∼q\sim \mathrm { p } \wedge \sim \mathrm { q }∼p∧∼q is equivalent to ∼(p∨q)\sim ( \mathrm { p } \vee \mathrm { q } )∼(p∨q) .

Solve the problem. -Given that p∧q\mathrm { p } \wedge \mathrm { q }p∧q is true, what can you conclude about the truth values of p\mathrm { p }p and q\mathrm { q }q ?

When using a truth table, the statement q∧∼pq \wedge \sim pq∧∼p is equivalent to ∼p→∼q\sim p \rightarrow \sim q∼p→∼q .

Decide whether the statement is true or false. - For every real number x,x<6 and x>5. \text { For every real number } x , x < 6 \text { and } x > 5 \text {. } For every real number x,x<6 and x>5.

Decide whether the statement is compound. -Today is not Thursday.

Decide whether or not the following is a statement. -July 4 was a Monday.

When using a truth table, the statement ∼q∧p is equivalent to ∼q→p. \text { When using a truth table, the statement } \sim q \wedge p \text { is equivalent to } \sim q \rightarrow p \text {. } When using a truth table, the statement ∼q∧p is equivalent to ∼q→p.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -Cats chase mice.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If you wear a tie, then you look natty. You do not look natty.‾\underline { \text {You do not look natty.} }You do not look natty.​ You are not wearing a tie.

Construct a truth table for the statement. - (∼p→q)→(q→∼r)(\sim p \rightarrow q) \rightarrow(q \rightarrow \sim r)(∼p→q)→(q→∼r)

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

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - $\sim ( p \wedge q ) \wedge ( r \vee \sim q )$

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If the bell rings, then we answer the door. $\underline { \text {The bell rings.} }$ We answer the door.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If I'm hungry, then I will eat. $\underline { \text {I'm not hungry.} }$ I will not eat.

When using a truth table, the statement $\sim \mathrm { p } \wedge \sim \mathrm { q }$ is equivalent to $\sim ( \mathrm { p } \vee \mathrm { q } )$ .

Solve the problem. -Given that $\mathrm { p } \wedge \mathrm { q }$ is true, what can you conclude about the truth values of $\mathrm { p }$ and $\mathrm { q }$ ?

When using a truth table, the statement $q \wedge \sim p$ is equivalent to $\sim p \rightarrow \sim q$ .

Decide whether the statement is true or false. - $\text { For every real number } x , x < 6 \text { and } x > 5 \text {. }$

$\text { When using a truth table, the statement } \sim q \wedge p \text { is equivalent to } \sim q \rightarrow p \text {. }$

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If you wear a tie, then you look natty. $\underline { \text {You do not look natty.} }$ You are not wearing a tie.

Construct a truth table for the statement. - $(\sim p \rightarrow q) \rightarrow(q \rightarrow \sim r)$