Question 1

The argument has a true conclusion. Identify the argument as valid or invalid.
-All dogs have fur.
$\underline { \text {All cats have fur} }$
A cat is not a dog.

Accepted Answer

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

Question 2

Use De Morgan's laws to write the negation of the statement.
-Cats are lazy or dogs aren't friendly.

Accepted Answer

A) Cats aren't lazy and dogs are friendly. 
B) Cats aren't lazy or dogs aren't friendly. 
C) Cats aren't lazy or dogs are friendly. 
D) Cats are lazy and dogs are friendly. 
A) Cats aren't lazy and dogs are friendly. 
B) Cats aren't lazy or dogs aren't friendly. 
C) Cats aren't lazy or dogs are friendly. 
D) Cats are lazy and dogs are friendly.

Question 3

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".
-$7 + 3 = 17 \underline\vee 7 + 8 = 15$

Accepted Answer

A) True 
 B)False

Question 4

Determine whether the argument is valid or invalid.
-If I were your friend and you were my soul mate, then I'd never stop liking you. I've stopped liking you. Therefore, I am not your friend or you were not my soul mate.

Accepted Answer

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

Question 5

Label the pair of statements as either contrary or consistent.
-He is an accountant. He loves to dance.

Accepted Answer

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

Question 6

Decide whether or not the following is a statement.
-Mary has a cat.

Accepted Answer

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

Question 7

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 the food is good or if I eat too much, then I'll exercise.

Accepted Answer

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

Question 8

Decide whether the statement is compound.
-He's from England and he doesn't drink tea.

Accepted Answer

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

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

Tell whether the conditional statement is true or false.
-Here T represents a true statement. $\mathrm { T } \rightarrow ( 2 = 7 )$

Accepted Answer

A) True 
 B)False

Question 11

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols.
-Jim does not play football and Michael does not play basketball.

Accepted Answer

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

Question 12

$\text { If } \mathrm { q } \text { is true then the statement } ( \mathrm { p } \vee \sim \mathrm { q } ) \rightarrow \text { must be true. }$

Accepted Answer

A) True 
 B)False

Question 13

Decide whether the statement is true or false.
-$\text { For every counting number } x , x \geq 1 \text { or } x = x ^ { 2 } \text {. }$

Accepted Answer

A) True 
 B)False

Question 14

Label the pair of statements as either contrary or consistent.
-The printer is not working right. The printer is broken.

Accepted Answer

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

Question 15

Write a negation of the inequality. Do not use a slash symbol.
-$x \leq 12$

Accepted Answer

A)  $x > - 12$ 
B)  $x \leq - 12$ 
C)  $x \geq 12$ 
D)  $x > 12$ 
A)  $x > - 12$ 
B)  $x \leq - 12$ 
C)  $x \geq 12$ 
D)  $x > 12$

Question 16

Decide whether the statement is compound.
-She was singing a Simon and Garfunkel song.

Accepted Answer

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

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

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

Accepted Answer

A) 
$\begin{array}{cccc}
\mathrm{r} & \mathrm{s} & \mathrm{C} & \mathrm{r} \vee \sim(\mathrm{s} \wedge \mathrm{c}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
B) 
$\begin{array}{cccc}
\mathrm{r} & \mathrm{s} & \mathrm{c} & \mathrm{r} \vee \sim(\mathrm{s} \wedge \mathrm{c}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$ 
A) 
$\begin{array}{cccc}
\mathrm{r} & \mathrm{s} & \mathrm{C} & \mathrm{r} \vee \sim(\mathrm{s} \wedge \mathrm{c}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
B) 
$\begin{array}{cccc}
\mathrm{r} & \mathrm{s} & \mathrm{c} & \mathrm{r} \vee \sim(\mathrm{s} \wedge \mathrm{c}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$

Question 19

Solve the logic puzzle by using a grid.
-Summer forgot in which chapter she has math homework. She knows it is within chapters 3 to 7 and deals with exponents. She knows that her homework is not from chapter 3. Last month they
Worked on chapter 4 so they're at least two chapters ahead by now. The final will not be for another
Month. She estimates that they do two chapters a month and the book has 8 chapters. When the
Final comes, they will have just finished the entire book. Which chapter should Summer look in to
Do the homework assignment?

Accepted Answer

A) Chapter 4 
B) Chapter 7 
C) Chapter 5 
D) Chapter 6 
A) Chapter 4 
B) Chapter 7 
C) Chapter 5 
D) Chapter 6

Question 20

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols.
-It is not the case that Jim does not play football and Michael does not play basketball.

Accepted Answer

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

The argument has a true conclusion. Identify the argument as valid or invalid. -All dogs have fur. $\underline { \text {All cats have fur} }$ A cat is not a dog.

Use De Morgan's laws to write the negation of the statement. -Cats are lazy or dogs aren't friendly.

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". - $7 + 3 = 17 \underline\vee 7 + 8 = 15$

Determine whether the argument is valid or invalid. -If I were your friend and you were my soul mate, then I'd never stop liking you. I've stopped liking you. Therefore, I am not your friend or you were not my soul mate.

Label the pair of statements as either contrary or consistent. -He is an accountant. He loves to dance.

Decide whether or not the following is a statement. -Mary has a cat.

Write the compound statement in symbols. Let $r =$ "The food is good." p= "I eat too much." q= "I'll exercise." -If the food is good or if I eat too much, then I'll exercise.

Decide whether the statement is compound. -He's from England and he doesn't drink tea.

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

Tell whether the conditional statement is true or false. -Here T represents a true statement. $\mathrm { T } \rightarrow ( 2 = 7 )$

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -Jim does not play football and Michael does not play basketball.

$\text { If } \mathrm { q } \text { is true then the statement } ( \mathrm { p } \vee \sim \mathrm { q } ) \rightarrow \text { must be true. }$

Decide whether the statement is true or false. - $\text { For every counting number } x , x \geq 1 \text { or } x = x ^ { 2 } \text {. }$

Label the pair of statements as either contrary or consistent. -The printer is not working right. The printer is broken.

Write a negation of the inequality. Do not use a slash symbol. - $x \leq 12$

Decide whether the statement is compound. -She was singing a Simon and Garfunkel song.

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

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

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -It is not the case that Jim does not play football and Michael does not play 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

The argument has a true conclusion. Identify the argument as valid or invalid. -All dogs have fur. All cats have fur‾\underline { \text {All cats have fur} }All cats have fur​ A cat is not a dog.

Use De Morgan's laws to write the negation of the statement. -Cats are lazy or dogs aren't friendly.

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". - 7+3=17∨‾7+8=157 + 3 = 17 \underline\vee 7 + 8 = 157+3=17∨​7+8=15

Determine whether the argument is valid or invalid. -If I were your friend and you were my soul mate, then I'd never stop liking you. I've stopped liking you. Therefore, I am not your friend or you were not my soul mate.

Label the pair of statements as either contrary or consistent. -He is an accountant. He loves to dance.

Decide whether or not the following is a statement. -Mary has a cat.

Write the compound statement in symbols. Let r=r =r= "The food is good." p= "I eat too much." q= "I'll exercise." -If the food is good or if I eat too much, then I'll exercise.

Decide whether the statement is compound. -He's from England and he doesn't drink tea.

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 [ ( \sim p \wedge \sim q ) \vee \sim q ]∼[(∼p∧∼q)∨∼q]

Tell whether the conditional statement is true or false. -Here T represents a true statement. T→(2=7)\mathrm { T } \rightarrow ( 2 = 7 )T→(2=7)

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -Jim does not play football and Michael does not play basketball.

If q is true then the statement (p∨∼q)→ must be true. \text { If } \mathrm { q } \text { is true then the statement } ( \mathrm { p } \vee \sim \mathrm { q } ) \rightarrow \text { must be true. } If q is true then the statement (p∨∼q)→ must be true.

Decide whether the statement is true or false. - For every counting number x,x≥1 or x=x2. \text { For every counting number } x , x \geq 1 \text { or } x = x ^ { 2 } \text {. } For every counting number x,x≥1 or x=x2.

Label the pair of statements as either contrary or consistent. -The printer is not working right. The printer is broken.

Write a negation of the inequality. Do not use a slash symbol. - x≤12x \leq 12x≤12

Decide whether the statement is compound. -She was singing a Simon and Garfunkel song.

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

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

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -It is not the case that Jim does not play football and Michael does not play 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

The argument has a true conclusion. Identify the argument as valid or invalid. -All dogs have fur. $\underline { \text {All cats have fur} }$ A cat is not a dog.

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". - $7 + 3 = 17 \underline\vee 7 + 8 = 15$

Write the compound statement in symbols. Let $r =$ "The food is good." p= "I eat too much." q= "I'll exercise." -If the food is good or if I eat too much, then I'll exercise.

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

Tell whether the conditional statement is true or false. -Here T represents a true statement. $\mathrm { T } \rightarrow ( 2 = 7 )$

$\text { If } \mathrm { q } \text { is true then the statement } ( \mathrm { p } \vee \sim \mathrm { q } ) \rightarrow \text { must be true. }$

Decide whether the statement is true or false. - $\text { For every counting number } x , x \geq 1 \text { or } x = x ^ { 2 } \text {. }$

Write a negation of the inequality. Do not use a slash symbol. - $x \leq 12$

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

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