Question 1

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

Accepted Answer

A) 4 
B) 8 
C) 9 
D) 16 
A) 4 
B) 8 
C) 9 
D) 16

Question 2

Determine if the argument is valid or a fallacy. Give a reason to justify answer.
-If you eat well, you will be well.
$\underline { \text {If you are well, you will be happy.} }$
If you eat well, you will be happy.

Accepted Answer

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

Question 3

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument.
-If I get robbed, I will go to court. I got robbed.

Accepted Answer

A) I will go to court. 
B) I will not go to court. 
C) I will not get robbed in court. 
D) I will get robbed in court. 
A) I will go to court. 
B) I will not go to court. 
C) I will not get robbed in court. 
D) I will get robbed in court.

Question 4

Convert the symbolic compound statement into words.
-p represents the statement "Her name is Lisa." q represents the statement "She lives in Chicago." Translate the following compound statement into words: $\sim p$

Accepted Answer

A)  She does not live in Chicago. 
B)  It is true her name is Lisa. 
C)  Her name is Teresa. 
D)  Her name is not Lisa. 
A)  She does not live in Chicago. 
B)  It is true her name is Lisa. 
C)  Her name is Teresa. 
D)  Her name is not Lisa.

Question 5

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

Accepted Answer

A) True 
 B)False

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 the hammer is on the floor, the baby will get hurt.

Accepted Answer

A) If the hammer is on the floor, the baby will not get hurt. 
B) The hammer is not on the floor and the baby will get hurt. 
C) The hammer is not on the floor and the baby will not get hurt. 
D) The hammer is on the floor and the baby will not get hurt. 
A) If the hammer is on the floor, the baby will not get hurt. 
B) The hammer is not on the floor and the baby will get hurt. 
C) The hammer is not on the floor and the baby will not get hurt. 
D) The hammer is on the floor and the baby will not get hurt.

Question 7

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

Accepted Answer

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

Question 8

Given p is true, q is true, and r is false, find the truth value of the statement.
-$\sim q \rightarrow r$

Accepted Answer

A) True 
 B)False

Question 9

Use an Euler diagram to determine whether the argument is valid or invalid.
-Some TV shows are comedies.
$\underline { \text { All comedies are hits. } }$
Some TV shows are hits.

Accepted Answer

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

Question 10

Label the pair of statements as either contrary or consistent.
-She likes coffee. She likes tea.

Accepted Answer

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

Question 11

Use a truth table to determine whether the argument is valid.
-$\begin{array}{l}
p \rightarrow \sim q \
q \rightarrow \sim p \
\hline p \vee q
\end{array}$

Accepted Answer

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

Question 12

Rewrite the statement in the form "if p, then q".
-Practice is necessary for making the team.

Accepted Answer

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

Question 13

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 you can't win the set, then you don't bother playing.

Accepted Answer

A) You can't win the set so you don't bother playing. 
B) You can't win the set and you do bother playing. 
C) You can win the set or you do bother playing. 
D) You can win the set or you don't bother playing. 
A) You can't win the set so you don't bother playing. 
B) You can't win the set and you do bother playing. 
C) You can win the set or you do bother playing. 
D) You can win the set or you don't bother playing.

Question 14

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-A ship can't sail on land.

Accepted Answer

A) If this is a ship, then it can sail on land. 
B) If this is a ship, then it can't sail on land. 
C) If this is not land, then a ship can't sail. 
D) A ship can't sail on land. 
A) If this is a ship, then it can sail on land. 
B) If this is a ship, then it can't sail on land. 
C) If this is not land, then a ship can't sail. 
D) A ship can't sail on land.

Question 15

Write the converse, inverse, or contrapositive of the statement as requested.
-$\mathrm { q } \rightarrow ( \sim \mathrm { p } \wedge \mathrm { r } )$
Contrapositive
(Use one of De Morgan's laws)

Accepted Answer

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

Question 16

Decide whether the statement is true or false.
-Every rational number is an integer.

Accepted Answer

A) True 
 B)False

Question 17

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument.
-Hard workers sweat. Sweat brings on a chill. Anyone who doesn't have a cold never felt a chill. Anyone who works doesn't have a cold.

Accepted Answer

A) Anyone who has a cold works hard. 
B) Hard workers don't get colds. 
C) Anyone who sweats works hard. 
D) Hard workers don't go to work. 
A) Anyone who has a cold works hard. 
B) Hard workers don't get colds. 
C) Anyone who sweats works hard. 
D) Hard workers don't go to work.

Question 18

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

Accepted Answer

A) True 
 B)False

Question 19

Convert the symbolic compound statement into words.
-p represents the statement: " $x  1$ "
Translate the following compound statement into words: $\mathrm { p } \vee\sim \mathrm { q }$

Accepted Answer

A)  $\mathrm { x }$ is less than 1 and $\mathrm { y }$ is not greater than 1 . 
B)  $x$ is less than 1 or $y$ is less than 1 . 
C)  $x$ is less than 1 or $y$ is not greater than 1 . 
D)  $x$ is not less than 1 and $y$ is not less than 1 
A)  $\mathrm { x }$ is less than 1 and $\mathrm { y }$ is not greater than 1 . 
B)  $x$ is less than 1 or $y$ is less than 1 . 
C)  $x$ is less than 1 or $y$ is not greater than 1 . 
D)  $x$ is not less than 1 and $y$ is not less than 1

Question 20

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

Accepted Answer

The answer of Write a logical statement representing the following...

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

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If you eat well, you will be well. $\underline { \text {If you are well, you will be happy.} }$ If you eat well, you will be happy.

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -If I get robbed, I will go to court. I got robbed.

Convert the symbolic compound statement into words. -p represents the statement "Her name is Lisa." q represents the statement "She lives in Chicago." Translate the following compound statement into words: $\sim p$

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

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$ -If the hammer is on the floor, the baby will get hurt.

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. - $\sim q \rightarrow r$

Use an Euler diagram to determine whether the argument is valid or invalid. -Some TV shows are comedies. $\underline { \text { All comedies are hits. } }$ Some TV shows are hits.

Label the pair of statements as either contrary or consistent. -She likes coffee. She likes tea.

Use a truth table to determine whether the argument is valid. - p\rightarrow\simq q\rightarrow\simp p\veeq

Rewrite the statement in the form "if p, then q". -Practice is necessary for making the team.

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 you can't win the set, then you don't bother playing.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -A ship can't sail on land.

Write the converse, inverse, or contrapositive of the statement as requested. - $\mathrm { q } \rightarrow ( \sim \mathrm { p } \wedge \mathrm { r } )$ Contrapositive (Use one of De Morgan's laws)

Decide whether the statement is true or false. -Every rational number is an integer.

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -Hard workers sweat. Sweat brings on a chill. Anyone who doesn't have a cold never felt a chill. Anyone who works doesn't have a cold.

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

Convert the symbolic compound statement into words. -p represents the statement: " $x < 1$ " q represents the statement: " $y > 1$ " Translate the following compound statement into words: $\mathrm { p } \vee\sim \mathrm { q }$

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

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

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Exam 3: Introduction to Logic

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

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If you eat well, you will be well. If you are well, you will be happy.‾\underline { \text {If you are well, you will be happy.} }If you are well, you will be happy.​ If you eat well, you will be happy.

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -If I get robbed, I will go to court. I got robbed.

Convert the symbolic compound statement into words. -p represents the statement "Her name is Lisa." q represents the statement "She lives in Chicago." Translate the following compound statement into words: ∼p\sim p∼p

Given p is true, q is true, and r is false, find the truth value of the statement. - (∼p→∼q)∧(p→∼r)( \sim \mathrm { p } \rightarrow \sim \mathrm { q } ) \wedge ( \mathrm { p } \rightarrow \sim \mathrm { r } )(∼p→∼q)∧(p→∼r)

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. - ∼q→r\sim q \rightarrow r∼q→r

Use an Euler diagram to determine whether the argument is valid or invalid. -Some TV shows are comedies. All comedies are hits. ‾\underline { \text { All comedies are hits. } } All comedies are hits. ​ Some TV shows are hits.

Label the pair of statements as either contrary or consistent. -She likes coffee. She likes tea.

Use a truth table to determine whether the argument is valid. - p\rightarrow\simq q\rightarrow\simp p\veeq

Rewrite the statement in the form "if p, then q". -Practice is necessary for making the team.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -A ship can't sail on land.

Write the converse, inverse, or contrapositive of the statement as requested. - q→(∼p∧r)\mathrm { q } \rightarrow ( \sim \mathrm { p } \wedge \mathrm { r } )q→(∼p∧r) Contrapositive (Use one of De Morgan's laws)

Decide whether the statement is true or false. -Every rational number is an integer.

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -Hard workers sweat. Sweat brings on a chill. Anyone who doesn't have a cold never felt a chill. Anyone who works doesn't have a cold.

Convert the symbolic compound statement into words. -p represents the statement: " x<1x < 1x<1 " q represents the statement: " y>1y > 1y>1 " Translate the following compound statement into words: p∨∼q\mathrm { p } \vee\sim \mathrm { q }p∨∼q

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

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

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If you eat well, you will be well. $\underline { \text {If you are well, you will be happy.} }$ If you eat well, you will be happy.

Convert the symbolic compound statement into words. -p represents the statement "Her name is Lisa." q represents the statement "She lives in Chicago." Translate the following compound statement into words: $\sim p$

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

Given p is true, q is true, and r is false, find the truth value of the statement. - $\sim q \rightarrow r$

Use an Euler diagram to determine whether the argument is valid or invalid. -Some TV shows are comedies. $\underline { \text { All comedies are hits. } }$ Some TV shows are hits.

Write the converse, inverse, or contrapositive of the statement as requested. - $\mathrm { q } \rightarrow ( \sim \mathrm { p } \wedge \mathrm { r } )$ Contrapositive (Use one of De Morgan's laws)

Convert the symbolic compound statement into words. -p represents the statement: " $x < 1$ " q represents the statement: " $y > 1$ " Translate the following compound statement into words: $\mathrm { p } \vee\sim \mathrm { q }$

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