Question 1

Decide whether or not the following is a statement.
-8 + 10 = 19

Accepted Answer

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

Question 2

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols.
-Neither Jim plays football nor Michael plays basketball.

Accepted Answer

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

Question 3

Convert the symbolic compound statement into words.
-p represents the statement "It's Monday." q represents the statement "It's raining today."
Translate the following compound statement into words: $\sim \mathrm { p } \vee \sim \mathrm { q }$

Accepted Answer

A) It's Monday or it's raining today. 
B) It's Monday and it's raining today. 
C) It's not Monday or it's not raining today. 
D) It's not Monday and it's not raining today. 
A) It's Monday or it's raining today. 
B) It's Monday and it's raining today. 
C) It's not Monday or it's not raining today. 
D) It's not Monday and it's not raining today.

Question 4

Use an Euler diagram to determine whether the argument is valid or invalid.
-All businessmen wear suits.
$\underline { \text { Aaron wears a suit. } }$
Aaron is a businessman.

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

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

Accepted Answer

A) 8 
B) 2 
C) 16 
D) 4 
A) 8 
B) 2 
C) 16 
D) 4

Question 7

Use De Morgan's laws to write the negation of the statement.
-$3 < 7$ or $7 \neq 12$

Accepted Answer

A)  $3 \geq 7$ and $7 = 12$ 
B)  $3 \geq 7$ or $7 \neq 12$ 
C)  $3 \geq 7$ or $7 = 12$ 
D)  $3 < 7$ or $7 = 12$ 
A)  $3 \geq 7$ and $7 = 12$ 
B)  $3 \geq 7$ or $7 \neq 12$ 
C)  $3 \geq 7$ or $7 = 12$ 
D)  $3 < 7$ or $7 = 12$

Question 8

Decide whether the statement is true or false.
-$\text { For some real number } x , x ^ { 2 } + 5 x - 6 = 0 \text { and } | x - 5 | > 3$

Accepted Answer

A) True 
 B)False

Question 9

Rewrite the statement in the form "if p, then q".
-A regular hexagon is a six-sided figure .

Accepted Answer

A) If the figure is a regular hexagon, then it is a six-sided figure. 
B) If the figure is a regular hexagon, then it is not a six-sided figure. 
C) If the figure is a six-sided figure, then it is a regular hexagon. 
D) If the figure is not a regular hexagon, then it is not a six-sided figure. 
A) If the figure is a regular hexagon, then it is a six-sided figure. 
B) If the figure is a regular hexagon, then it is not a six-sided figure. 
C) If the figure is a six-sided figure, then it is a regular hexagon. 
D) If the figure is not a regular hexagon, then it is not a six-sided figure.

Question 10

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument.
-It is either day or night. If it is daytime, then the squirrels are scurrying. It is not nighttime.

Accepted Answer

A) Squirrels do not scurry during the day. 
B) The squirrels are not scurrying. 
C) The squirrels are scurrying. 
D) Squirrels do not scurry at night. 
A) Squirrels do not scurry during the day. 
B) The squirrels are not scurrying. 
C) The squirrels are scurrying. 
D) Squirrels do not scurry at night.

Question 11

Solve the logic puzzle by using a grid.
-Four friends, Pete, Martha, Steve, and Rosa, own dogs. They discover that two of them own the same kind of dog. Pete does not have a bulldog. Rosa and Steve don't have the same kind of dog
But both their dogs have short hair. Martha is allergic to the hair of a golden retriever. Rosa's dog is
Tall and thin. Pete's mother doesn't let his dog on the couch because the sheddings are too
Noticeable. Martha's dog is very short. The dogs are golden retriever, dalmation and bulldog. Match
Friend and dog.

Accepted Answer

A) Pete - bulldog, Martha and Rosa - dalmation, Steve - golden retriever 
B) Steve - bulldog, Martha and Pete - golden retriever, Rosa - dalmation 
C) Pete - golden retriever, Martha and Steve - bulldog, Rosa - dalmation 
D) Rosa - golden retriever, Steve - bulldog, Martha and Pete - dalmation 
A) Pete - bulldog, Martha and Rosa - dalmation, Steve - golden retriever 
B) Steve - bulldog, Martha and Pete - golden retriever, Rosa - dalmation 
C) Pete - golden retriever, Martha and Steve - bulldog, Rosa - dalmation 
D) Rosa - golden retriever, Steve - bulldog, Martha and Pete - dalmation

Question 12

Write a negation for the statement.
-No fifth graders play soccer.

Accepted Answer

A) Not all fifth graders play soccer. 
B) At least one fifth grader plays soccer. 
C) All fifth graders play soccer. 
D) No fifth grader does not play soccer. 
A) Not all fifth graders play soccer. 
B) At least one fifth grader plays soccer. 
C) All fifth graders play soccer. 
D) No fifth grader does not play soccer.

Question 13

Decide whether the statement is true or false.
-$\text { For some real number } p , | p - 9 | < 0 \text { or } | 9 - p | < 0 \text {. }$

Accepted Answer

A) True 
 B)False

Question 14

Label the pair of statements as either contrary or consistent.
-Rosa graduated from high school last year. Rosa has an advanced degree.

Accepted Answer

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

Question 15

Write the compound statement in symbols. Let $r =$ "The food is good."
$\begin{array} { l } 
p = \text { "I eat too much." } \
q = \text { "I'll exercise." }
\end{array}$
-The food is good and if I eat too much, then I'll exercise.

Accepted Answer

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

Question 16

Write a negation of the inequality. Do not use a slash symbol.
-$x > 69$

Accepted Answer

A)  $x = 69$ 
B)  $x < 69$ 
C)  $x \leq 69$ 
D)  $x < - 69$ 
A)  $x = 69$ 
B)  $x < 69$ 
C)  $x \leq 69$ 
D)  $x < - 69$

Question 17

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

Accepted Answer

A) True 
 B)False

Question 18

Decide whether the statement is true or false.
-Some whole numbers are not integers.

Accepted Answer

A) True 
 B)False

Question 19

Write the converse, inverse, or contrapositive of the statement as requested.
-If I pass, I'll party. Contrapositive

Accepted Answer

A) If I party, then I passed. 
B) If I don't pass, I won't party. 
C) I'll party if I pass. 
D) If I don't party, I didn't pass. 
A) If I party, then I passed. 
B) If I don't pass, I won't party. 
C) I'll party if I pass. 
D) If I don't party, I didn't pass.

Question 20

Decide whether the statement is compound.
-$21 + 33 \neq 60$

Accepted Answer

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

Decide whether or not the following is a statement. -8 + 10 = 19

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -Neither Jim plays football nor Michael plays basketball.

Convert the symbolic compound statement into words. -p represents the statement "It's Monday." q represents the statement "It's raining today." Translate the following compound statement into words: $\sim \mathrm { p } \vee \sim \mathrm { q }$

Use an Euler diagram to determine whether the argument is valid or invalid. -All businessmen wear suits. $\underline { \text { Aaron wears a suit. } }$ Aaron is a businessman.

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

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

Use De Morgan's laws to write the negation of the statement. - $3 < 7$ or $7 \neq 12$

Decide whether the statement is true or false. - $\text { For some real number } x , x ^ { 2 } + 5 x - 6 = 0 \text { and } | x - 5 | > 3$

Rewrite the statement in the form "if p, then q". -A regular hexagon is a six-sided figure .

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -It is either day or night. If it is daytime, then the squirrels are scurrying. It is not nighttime.

Write a negation for the statement. -No fifth graders play soccer.

Decide whether the statement is true or false. - $\text { For some real number } p , | p - 9 | < 0 \text { or } | 9 - p | < 0 \text {. }$

Label the pair of statements as either contrary or consistent. -Rosa graduated from high school last year. Rosa has an advanced degree.

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

Write a negation of the inequality. Do not use a slash symbol. - $x > 69$

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

Decide whether the statement is true or false. -Some whole numbers are not integers.

Write the converse, inverse, or contrapositive of the statement as requested. -If I pass, I'll party. Contrapositive

Decide whether the statement is compound. - $21 + 33 \neq 60$

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

Decide whether or not the following is a statement. -8 + 10 = 19

Let p represent the statement, "Jim plays football", and let q represent the statement "Michael plays basketball". Convert the compound statement into symbols. -Neither Jim plays football nor Michael plays basketball.

Convert the symbolic compound statement into words. -p represents the statement "It's Monday." q represents the statement "It's raining today." Translate the following compound statement into words: ∼p∨∼q\sim \mathrm { p } \vee \sim \mathrm { q }∼p∨∼q

Use an Euler diagram to determine whether the argument is valid or invalid. -All businessmen wear suits. Aaron wears a suit. ‾\underline { \text { Aaron wears a suit. } } Aaron wears a suit. ​ Aaron is a businessman.

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 \rightarrow ( p \wedge q )r→(p∧q)

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

Use De Morgan's laws to write the negation of the statement. - 3<73 < 73<7 or 7≠127 \neq 127=12

Decide whether the statement is true or false. - For some real number x,x2+5x−6=0 and ∣x−5∣>3\text { For some real number } x , x ^ { 2 } + 5 x - 6 = 0 \text { and } | x - 5 | > 3 For some real number x,x2+5x−6=0 and ∣x−5∣>3

Rewrite the statement in the form "if p, then q". -A regular hexagon is a six-sided figure .

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -It is either day or night. If it is daytime, then the squirrels are scurrying. It is not nighttime.

Write a negation for the statement. -No fifth graders play soccer.

Decide whether the statement is true or false. - For some real number p,∣p−9∣<0 or ∣9−p∣<0. \text { For some real number } p , | p - 9 | < 0 \text { or } | 9 - p | < 0 \text {. } For some real number p,∣p−9∣<0 or ∣9−p∣<0.

Label the pair of statements as either contrary or consistent. -Rosa graduated from high school last year. Rosa has an advanced degree.

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

Write a negation of the inequality. Do not use a slash symbol. - x>69x > 69x>69

Decide whether the statement is true or false. -Some whole numbers are not integers.

Write the converse, inverse, or contrapositive of the statement as requested. -If I pass, I'll party. Contrapositive

Decide whether the statement is compound. - 21+33≠6021 + 33 \neq 6021+33=60

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

Convert the symbolic compound statement into words. -p represents the statement "It's Monday." q represents the statement "It's raining today." Translate the following compound statement into words: $\sim \mathrm { p } \vee \sim \mathrm { q }$

Use an Euler diagram to determine whether the argument is valid or invalid. -All businessmen wear suits. $\underline { \text { Aaron wears a suit. } }$ Aaron is a businessman.

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

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

Use De Morgan's laws to write the negation of the statement. - $3 < 7$ or $7 \neq 12$

Decide whether the statement is true or false. - $\text { For some real number } x , x ^ { 2 } + 5 x - 6 = 0 \text { and } | x - 5 | > 3$

Decide whether the statement is true or false. - $\text { For some real number } p , | p - 9 | < 0 \text { or } | 9 - p | < 0 \text {. }$

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

Write a negation of the inequality. Do not use a slash symbol. - $x > 69$

Decide whether the statement is compound. - $21 + 33 \neq 60$