Question 1

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

Accepted Answer

A) True 
 B)False

Question 2

Use De Morgan's laws to write the negation of the statement.
-$9 + 2 = 11$ and $7 - 4 \neq 3$

Accepted Answer

A)  $9 + 2 \neq 11$ and $7 - 4 = 3$ 
B)  $9 + 2 = 11$ or $7 - 4 \neq 3$ 
C)  $9 + 2 \neq 11$ or $7 - 4 = 3$ 
D)  $9 + 2 = 11$ and $7 - 4 = 3$ 
A)  $9 + 2 \neq 11$ and $7 - 4 = 3$ 
B)  $9 + 2 = 11$ or $7 - 4 \neq 3$ 
C)  $9 + 2 \neq 11$ or $7 - 4 = 3$ 
D)  $9 + 2 = 11$ and $7 - 4 = 3$

Question 3

Write the compound statement in words. Let $r =$ "The puppy is trained."
$\mathrm { p } =$ "The puppy behaves well."
$q =$ "His owners are happy."
-$r \wedge ( p \rightarrow q )$

Accepted Answer

A) If the puppy is trained then the puppy behaves well, and his owners are happy. 
B) The puppy is trained, and if the puppy behaves well then his owners are happy. 
C) The puppy is trained if the puppy behaves well and his owners are happy. 
D) The puppy is trained, or if the puppy behaves well then his owners are happy. 
A) If the puppy is trained then the puppy behaves well, and his owners are happy. 
B) The puppy is trained, and if the puppy behaves well then his owners are happy. 
C) The puppy is trained if the puppy behaves well and his owners are happy. 
D) The puppy is trained, or if the puppy behaves well then his owners are happy.

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

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

Accepted Answer

A) 9 
B) 6 
C) 8 
D) 3 
A) 9 
B) 6 
C) 8 
D) 3

Question 6

Rewrite the statement in the form "if p, then q".
-Showing up at the party is sufficient to get a door prize.

Accepted Answer

A) If you don't show up at the party, then you will not get a door prize. 
B) If you show up at the party then you will get a door prize. 
C) If you got a door prize then you showed up at the party. 
D) If you get a door prize then you don't have to show up at the party. 
A) If you don't show up at the party, then you will not get a door prize. 
B) If you show up at the party then you will get a door prize. 
C) If you got a door prize then you showed up at the party. 
D) If you get a door prize then you don't have to show up at the party.

Question 7

Determine whether the argument is valid or invalid.
-If Cathy is a gambler, then she lives in Marine. Cathy lives in Marine and she loves horses. Therefore, if Cathy does not love horses, she is not a gambler.

Accepted Answer

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

Question 8

Decide whether the statement is true or false.
-Not every whole number is a real number.

Accepted Answer

A) True 
 B)False

Question 9

Find the truth value of the statement.
-$4 + 7 \neq 13 \text { if and only if } 8 \times 5 \neq 45 \text {. }$

Accepted Answer

A) True 
 B)False

Question 10

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

Accepted Answer

A) True 
 B)False

Question 11

Rewrite the statement in the form "if p, then q".
-I will be happy only if he calls.

Accepted Answer

A) If I am happy, then he must have called. 
B) If I am happy, then he won't call. 
C) If I am not happy, then he will call. 
D) If he calls, then I will be happy. 
A) If I am happy, then he must have called. 
B) If I am happy, then he won't call. 
C) If I am not happy, then he will call. 
D) If he calls, then I will be happy.

Question 12

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

Accepted Answer

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

Question 13

Rewrite the statement in the form "if p, then q".
-All numbers which are divisible by four are even numbers.

Accepted Answer

A) If a number is divisible by four, then it is even. 
B) If a number is even, then it is not divisible by four. 
C) If a number is even, then it is divisible by four. 
D) If a number is not divisible by four, then it is not even. 
A) If a number is divisible by four, then it is even. 
B) If a number is even, then it is not divisible by four. 
C) If a number is even, then it is divisible by four. 
D) If a number is not divisible by four, then it is not even.

Question 14

Convert the symbolic compound statement into words.
-p represents the statement : "Students are happy." q represents the statement: "Teachers are happy."
Translate the following compound statement into words: $\sim ( p \vee \sim q )$

Accepted Answer

A) Students are not happy and teachers are not happy. 
B) Students are not happy or teachers are not happy. 
C) It is not the case that students are happy or teachers are not happy. 
D) It is not the case that students are happy and teachers are not happy. 
A) Students are not happy and teachers are not happy. 
B) Students are not happy or teachers are not happy. 
C) It is not the case that students are happy or teachers are not happy. 
D) It is not the case that students are happy and teachers are not happy.

Question 15

Convert the symbolic compound statement into words.
-p represents the statement "It's raining in Chicago." q represents the statement "It's windy in Boston."
Translate the following compound statement into words: $p \vee q$

Accepted Answer

A) It's raining in Chicago or it's windy in Boston. 
B) It's raining in Chicago and it's windy in Boston. 
C) If it's raining in Chicago, it's not windy in Boston. 
D) It's not the case that it's raining in Chicago and windy in Boston. 
A) It's raining in Chicago or it's windy in Boston. 
B) It's raining in Chicago and it's windy in Boston. 
C) If it's raining in Chicago, it's not windy in Boston. 
D) It's not the case that it's raining in Chicago and windy in Boston.

Question 16

Decide whether the compound statement is true or false. The symbol for exclusive disjunction $\vee$ represents "one or the other is true, but not both".
-$9 + 4 = 13 \underline\vee 3 + 8 = 14$

Accepted Answer

A) True 
 B)False

Question 17

Decide whether or not the following is a statement.
-Not all flowers are roses.

Accepted Answer

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

Question 18

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

Question 19

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement.
-$[ ( \sim p \wedge \sim q ) \vee \sim q ]$

Accepted Answer

A) True 
 B)False

Question 20

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

Accepted Answer

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

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

Use De Morgan's laws to write the negation of the statement. - $9 + 2 = 11$ and $7 - 4 \neq 3$

Write the compound statement in words. Let $r =$ "The puppy is trained." $\mathrm { p } =$ "The puppy behaves well." $q =$ "His owners are happy." - $r \wedge ( p \rightarrow q )$

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

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

Rewrite the statement in the form "if p, then q". -Showing up at the party is sufficient to get a door prize.

Determine whether the argument is valid or invalid. -If Cathy is a gambler, then she lives in Marine. Cathy lives in Marine and she loves horses. Therefore, if Cathy does not love horses, she is not a gambler.

Decide whether the statement is true or false. -Not every whole number is a real number.

Find the truth value of the statement. - $4 + 7 \neq 13 \text { if and only if } 8 \times 5 \neq 45 \text {. }$

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

Rewrite the statement in the form "if p, then q". -I will be happy only if he calls.

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

Rewrite the statement in the form "if p, then q". -All numbers which are divisible by four are even numbers.

Convert the symbolic compound statement into words. -p represents the statement : "Students are happy." q represents the statement: "Teachers are happy." Translate the following compound statement into words: $\sim ( p \vee \sim q )$

Convert the symbolic compound statement into words. -p represents the statement "It's raining in Chicago." q represents the statement "It's windy in Boston." Translate the following compound statement into words: $p \vee q$

Decide whether the compound statement is true or false. The symbol for exclusive disjunction $\vee$ represents "one or the other is true, but not both". - $9 + 4 = 13 \underline\vee 3 + 8 = 14$

Decide whether or not the following is a statement. -Not all flowers are roses.

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

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement. - $[ ( \sim p \wedge \sim q ) \vee \sim q ]$

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

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

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Exam 3: Introduction to Logic

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

Use De Morgan's laws to write the negation of the statement. - 9+2=119 + 2 = 119+2=11 and 7−4≠37 - 4 \neq 37−4=3

Write the compound statement in words. Let r=r =r= "The puppy is trained." p=\mathrm { p } =p= "The puppy behaves well." q=q =q= "His owners are happy." - r∧(p→q)r \wedge ( p \rightarrow q )r∧(p→q)

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

Rewrite the statement in the form "if p, then q". -Showing up at the party is sufficient to get a door prize.

Determine whether the argument is valid or invalid. -If Cathy is a gambler, then she lives in Marine. Cathy lives in Marine and she loves horses. Therefore, if Cathy does not love horses, she is not a gambler.

Decide whether the statement is true or false. -Not every whole number is a real number.

Find the truth value of the statement. - 4+7≠13 if and only if 8×5≠45. 4 + 7 \neq 13 \text { if and only if } 8 \times 5 \neq 45 \text {. }4+7=13 if and only if 8×5=45.

When using a truth table, the statement q→p\mathrm { q } \rightarrow \mathrm { p }q→p is equivalent to ∼q∨p\sim \mathrm { q } \vee \mathrm { p }∼q∨p .

Rewrite the statement in the form "if p, then q". -I will be happy only if he calls.

Construct a truth table for the statement. - ∼(∼(q∨p))\sim ( \sim ( q \vee p ) )∼(∼(q∨p))

Rewrite the statement in the form "if p, then q". -All numbers which are divisible by four are even numbers.

Convert the symbolic compound statement into words. -p represents the statement : "Students are happy." q represents the statement: "Teachers are happy." Translate the following compound statement into words: ∼(p∨∼q)\sim ( p \vee \sim q )∼(p∨∼q)

Convert the symbolic compound statement into words. -p represents the statement "It's raining in Chicago." q represents the statement "It's windy in Boston." Translate the following compound statement into words: p∨qp \vee qp∨q

Decide whether the compound statement is true or false. The symbol for exclusive disjunction ∨\vee∨ represents "one or the other is true, but not both". - 9+4=13∨‾3+8=149 + 4 = 13 \underline\vee 3 + 8 = 149+4=13∨​3+8=14

Decide whether or not the following is a statement. -Not all flowers are roses.

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

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement. - [(∼p∧∼q)∨∼q][ ( \sim p \wedge \sim q ) \vee \sim q ][(∼p∧∼q)∨∼q]

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

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. - $( p \wedge \sim q ) \wedge r$

Use De Morgan's laws to write the negation of the statement. - $9 + 2 = 11$ and $7 - 4 \neq 3$

Write the compound statement in words. Let $r =$ "The puppy is trained." $\mathrm { p } =$ "The puppy behaves well." $q =$ "His owners are happy." - $r \wedge ( p \rightarrow q )$

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

Find the truth value of the statement. - $4 + 7 \neq 13 \text { if and only if } 8 \times 5 \neq 45 \text {. }$

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

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

Convert the symbolic compound statement into words. -p represents the statement : "Students are happy." q represents the statement: "Teachers are happy." Translate the following compound statement into words: $\sim ( p \vee \sim q )$

Convert the symbolic compound statement into words. -p represents the statement "It's raining in Chicago." q represents the statement "It's windy in Boston." Translate the following compound statement into words: $p \vee q$

Decide whether the compound statement is true or false. The symbol for exclusive disjunction $\vee$ represents "one or the other is true, but not both". - $9 + 4 = 13 \underline\vee 3 + 8 = 14$

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement. - $[ ( \sim p \wedge \sim q ) \vee \sim q ]$