Question 1

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

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 2

Solve the logic puzzle by using a grid.
-Joan has five skirts (black, brown, white, blue, and green)and five blouses (red, white, beige, pink, and black). She likes red and white together and likes the beige blouse with the brown skirt. She Doesn't like the way a dark blouse and a dark skirt look together. She does not like wearing her White blouse with her black nor green skirts. Considering that she will only match one blouse with Each skirt, what color blouse/skirt combinations will Joan have?

Accepted Answer

A) 
$\begin{array}{lll}
\text { Blouse } & \text { and } & \text { Skirt } \
\text { pink } & & \text { white } \
\text { black } & & \text { brown } \
\text { beige } & & \text { green } \
\text { red } & & \text { black } \
\text { white } & & \text { blue }
\end{array}$ 
B) 
$\begin{array}{lll}
\text { Blouse } & \text { and } & \text { Skirt } \
\text { beige } & & \text { black } \
\text { red } & & \text { brown } \
\text { white } & & \text { blue } \
\text { red } & & \text { green } \
\text { black } & & \text { white }
\end{array}$ 
C) 
$\begin{array}{lll}
\text { Blouse } & \text { and } & \text { Skirt } \
\text { pink } & & \text { black } \
\text { brown } & & \text { beige } \
\text { red } & & \text { white } \
\text { blue } & & \text { purple } \
\text { black } & & \text { green }
\end{array}$ 
D) 
$\begin{array}{lll}
\text { Blouse } & \text { and } & \text { Skirt } \
\text { pink } & & \text { black } \
\text { beige } && \text { brown } \
\text { red } & & \text { white } \
\text { white } && \text { blue } \
\text { black } & & \text { green }
\end{array}$ 
A) 
$\begin{array}{lll}
\text { Blouse } & \text { and } & \text { Skirt } \
\text { pink } & & \text { white } \
\text { black } & & \text { brown } \
\text { beige } & & \text { green } \
\text { red } & & \text { black } \
\text { white } & & \text { blue }
\end{array}$ 
B) 
$\begin{array}{lll}
\text { Blouse } & \text { and } & \text { Skirt } \
\text { beige } & & \text { black } \
\text { red } & & \text { brown } \
\text { white } & & \text { blue } \
\text { red } & & \text { green } \
\text { black } & & \text { white }
\end{array}$ 
C) 
$\begin{array}{lll}
\text { Blouse } & \text { and } & \text { Skirt } \
\text { pink } & & \text { black } \
\text { brown } & & \text { beige } \
\text { red } & & \text { white } \
\text { blue } & & \text { purple } \
\text { black } & & \text { green }
\end{array}$ 
D) 
$\begin{array}{lll}
\text { Blouse } & \text { and } & \text { Skirt } \
\text { pink } & & \text { black } \
\text { beige } && \text { brown } \
\text { red } & & \text { white } \
\text { white } && \text { blue } \
\text { black } & & \text { green }
\end{array}$

Question 3

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 plays basketball.

Accepted Answer

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

Question 4

Decide whether the statement is true or false.
-The absolute value of any number is positive.

Accepted Answer

A) True 
 B)False

Question 5

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$
-If $\mathrm { k } - 4 \leq 3$, then $\mathrm { k } \leq 7$.

Accepted Answer

A)  $\mathrm { k } - 4 > 3$ and $\mathrm { k } > 7$. 
B)  $k - 4 \leq 3$ so $k > 7$. 
C)  $k - 4 \leq 3$ and $k \geq 7$. 
D)  $k - 4 \leq 3$ and $k > 7$. 
A)  $\mathrm { k } - 4 > 3$ and $\mathrm { k } > 7$. 
B)  $k - 4 \leq 3$ so $k > 7$. 
C)  $k - 4 \leq 3$ and $k \geq 7$. 
D)  $k - 4 \leq 3$ and $k > 7$.

Question 6

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 or Michael plays basketball.

Accepted Answer

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

Question 7

Rewrite the statement in the form "if p, then q".
-No rational numbers are not real numbers.

Accepted Answer

A) If a number is a rational number, then it is a real number. 
B) If a number is a rational number, then it is not a real number. 
C) If a number is a real number, then it is a rational number. 
D) If a number is not a rational number, then it is not a real number. 
A) If a number is a rational number, then it is a real number. 
B) If a number is a rational number, then it is not a real number. 
C) If a number is a real number, then it is a rational number. 
D) If a number is not a rational number, then it is not a real number.

Question 8

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 your shoes need polishing, you take them to Jack's place.

Accepted Answer

A) Your shoes do not need polishing or you take them to Jack's place. 
B) Your shoes do not need polishing or you do not take them to Jack's place. 
C) Your shoes need polishing so you take them to Jack's place. 
D) Your shoes need polishing and you do not take them to Jack's place. 
A) Your shoes do not need polishing or you take them to Jack's place. 
B) Your shoes do not need polishing or you do not take them to Jack's place. 
C) Your shoes need polishing so you take them to Jack's place. 
D) Your shoes need polishing and you do not take them to Jack's place.

Question 9

Use an Euler diagram to determine whether the argument is valid or invalid.
-No even number is divisible by 5 .
$\underline { \text { 30 is an even number.} }$
30 is not divisible by 5 .

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Write a negation for the statement.
-She earns more than me.

Accepted Answer

A) She does not earn less than me. 
B) She does not earn more than me. 
C) She earns less than me. 
D) She earns the same as me. 
A) She does not earn less than me. 
B) She does not earn more than me. 
C) She earns less than me. 
D) She earns the same as me.

Question 12

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 find the right dress for the dinner, then you make one yourself.

Accepted Answer

A) You can find the right dress for the dinner or you make one yourself. 
B) You can find the right dress for the dinner so you do not make one yourself. 
C) You can't find the right dress for the dinner and you do not make one yourself. 
D) You can't find the right dress for the dinner or you do not make one yourself. 
A) You can find the right dress for the dinner or you make one yourself. 
B) You can find the right dress for the dinner so you do not make one yourself. 
C) You can't find the right dress for the dinner and you do not make one yourself. 
D) You can't find the right dress for the dinner or you do not make one yourself.

Question 13

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-No cars come from Iceland.

Accepted Answer

A) If it doesn't come from Iceland, then it is not a car. 
B) If it's not a car, then it comes from Iceland. 
C) No cars come from Iceland. 
D) If it is a car, then it doesn't come from Iceland. 
A) If it doesn't come from Iceland, then it is not a car. 
B) If it's not a car, then it comes from Iceland. 
C) No cars come from Iceland. 
D) If it is a car, then it doesn't come from Iceland.

Question 14

Determine if the argument is valid or a fallacy. Give a reason to justify answer.
-If it rains, then the squirrels hide.
$\underline { \text {The squirrels are hiding.} }$
You got salad.
It is raining.

Accepted Answer

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

Question 15

Decide whether or not the following is a statement.
-Do you like this color?

Accepted Answer

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

Question 16

Use an Euler diagram to determine whether the argument is valid or invalid.
-All tigers are felines.
All felines are mammals.
$\underline { \text { All mammals nurse their young.} }$
All tigers nurse their young.

Accepted Answer

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

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

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

Accepted Answer

A) The puppy is not trained and his owners are not happy. 
B) The puppy is trained or his owners are happy. 
C) It is not the case that if the puppy is trained then his owners are happy. 
D) If the puppy is not trained then his owners are not happy. 
A) The puppy is not trained and his owners are not happy. 
B) The puppy is trained or his owners are happy. 
C) It is not the case that if the puppy is trained then his owners are happy. 
D) If the puppy is not trained then his owners are not happy.

Question 19

The argument has a true conclusion. Identify the argument as valid or invalid.
-Rational numbers are real numbers.
$\underline { \text {Integers are rational numbers.} }$
Integers are real numbers.

Accepted Answer

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

Question 20

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

Accepted Answer

A) True 
 B)False

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

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 plays basketball.

Decide whether the statement is true or false. -The absolute value of any number is positive.

$\text { Write the negation of the conditional. Use the fact that the negation of } p \rightarrow q \text { is } p \wedge \sim q \text {. }$ -If $\mathrm { k } - 4 \leq 3$ , then $\mathrm { k } \leq 7$ .

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 or Michael plays basketball.

Rewrite the statement in the form "if p, then q". -No rational numbers are not real numbers.

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 your shoes need polishing, you take them to Jack's place.

Use an Euler diagram to determine whether the argument is valid or invalid. -No even number is divisible by 5 . $\underline { \text { 30 is an even number.} }$ 30 is not divisible by 5 .

Use a truth table to determine whether the argument is valid. - p\rightarrowq q q

Write a negation for the statement. -She earns more than me.

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 find the right dress for the dinner, then you make one yourself.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -No cars come from Iceland.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If it rains, then the squirrels hide. $\underline { \text {The squirrels are hiding.} }$ You got salad. It is raining.

Decide whether or not the following is a statement. -Do you like this color?

Use an Euler diagram to determine whether the argument is valid or invalid. -All tigers are felines. All felines are mammals. $\underline { \text { All mammals nurse their young.} }$ All tigers nurse their young.

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

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

The argument has a true conclusion. Identify the argument as valid or invalid. -Rational numbers are real numbers. $\underline { \text {Integers are rational numbers.} }$ Integers are real numbers.

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

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. - ∼(p∧q)→∼(p∨q)\sim(p \wedge q) \rightarrow \sim(p \vee q)∼(p∧q)→∼(p∨q)

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 plays basketball.

Decide whether the statement is true or false. -The absolute value of any number is positive.

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 or Michael plays basketball.

Rewrite the statement in the form "if p, then q". -No rational numbers are not real numbers.

Use an Euler diagram to determine whether the argument is valid or invalid. -No even number is divisible by 5 . 30 is an even number.‾\underline { \text { 30 is an even number.} } 30 is an even number.​ 30 is not divisible by 5 .

Use a truth table to determine whether the argument is valid. - p\rightarrowq q q

Write a negation for the statement. -She earns more than me.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -No cars come from Iceland.

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If it rains, then the squirrels hide. The squirrels are hiding.‾\underline { \text {The squirrels are hiding.} }The squirrels are hiding.​ You got salad. It is raining.

Decide whether or not the following is a statement. -Do you like this color?

Use an Euler diagram to determine whether the argument is valid or invalid. -All tigers are felines. All felines are mammals. All mammals nurse their young.‾\underline { \text { All mammals nurse their young.} } All mammals nurse their young.​ All tigers nurse their young.

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

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→∼q\sim \mathrm { r } \rightarrow \sim \mathrm { q }∼r→∼q

The argument has a true conclusion. Identify the argument as valid or invalid. -Rational numbers are real numbers. Integers are rational numbers.‾\underline { \text {Integers are rational numbers.} }Integers are rational numbers.​ Integers are real numbers.

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)\sim ( \sim p \wedge \sim q ) \vee ( \sim r \vee \sim p )∼(∼p∧∼q)∨(∼r∨∼p)

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. - $\sim(p \wedge q) \rightarrow \sim(p \vee q)$

Use an Euler diagram to determine whether the argument is valid or invalid. -No even number is divisible by 5 . $\underline { \text { 30 is an even number.} }$ 30 is not divisible by 5 .

Determine if the argument is valid or a fallacy. Give a reason to justify answer. -If it rains, then the squirrels hide. $\underline { \text {The squirrels are hiding.} }$ You got salad. It is raining.

Use an Euler diagram to determine whether the argument is valid or invalid. -All tigers are felines. All felines are mammals. $\underline { \text { All mammals nurse their young.} }$ All tigers nurse their young.

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

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

The argument has a true conclusion. Identify the argument as valid or invalid. -Rational numbers are real numbers. $\underline { \text {Integers are rational numbers.} }$ Integers are real numbers.

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