Question 1

Label the pair of statements as either contrary or consistent.
-Today is Friday. Tomorrow is Sunday.

Accepted Answer

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

Question 2

Write the converse, inverse, or contrapositive of the statement as requested.
-If I were young, I would be happy. Converse

Accepted Answer

A) If I were not happy, I would not be young. 
B) If I were young, I would not be happy. 
C) If I were not young, I would not be happy. 
D) If I were happy, I would be young. 
A) If I were not happy, I would not be young. 
B) If I were young, I would not be happy. 
C) If I were not young, I would not be happy. 
D) If I were happy, I would be young.

Question 3

The argument has a true conclusion. Identify the argument as valid or invalid.
-8 is a real number.
$\underline { \sqrt { 64 } \text {is a real number.} }$
8 is $\sqrt { 64 }$.

Accepted Answer

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

Question 4

Decide whether the statement is compound.
-Computers are very helpful to people.

Accepted Answer

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

Question 5

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: $p \wedge q$

Accepted Answer

A) Her name is Lisa and she lives in Chicago. 
B) Her name is Lisa or she lives in Chicago. 
C) If her name is Lisa, she lives in Chicago. 
D) Her name is Lisa and she doesn't live in Chicago. 
A) Her name is Lisa and she lives in Chicago. 
B) Her name is Lisa or she lives in Chicago. 
C) If her name is Lisa, she lives in Chicago. 
D) Her name is Lisa and she doesn't live in Chicago.

Question 6

Write a negation for the statement.
-Everyone is asleep.

Accepted Answer

A) Not everyone is asleep. 
B) Nobody is awake. 
C) Everyone is awake. 
D) Nobody is asleep. 
A) Not everyone is asleep. 
B) Nobody is awake. 
C) Everyone is awake. 
D) Nobody is asleep.

Question 7

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-I'll leave when he arrives.

Accepted Answer

A) If he arrives, then I'll leave. 
B) If I leave, then he will leave. 
C) If I will leave, then he'll arrive. 
D) I'll leave when he arrives. 
A) If he arrives, then I'll leave. 
B) If I leave, then he will leave. 
C) If I will leave, then he'll arrive. 
D) I'll leave when he arrives.

Question 8

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 not good, I won't eat too much.

Accepted Answer

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

Question 9

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, then I eat too much.

Accepted Answer

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

Question 10

Determine whether the argument is valid or invalid.
-Sam plays tennis or George is not a man. If George is not a man, then Betsy does not win the award. Betsy wins the award. Therefore, Sam does not play tennis.

Accepted Answer

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

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

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

Accepted Answer

A) If the puppy is not trained or the puppy does not behave well, then his owners are not happy. 
B) The puppy is not trained or the puppy does not behave well, and his owners are not happy. 
C) If the puppy is not trained then the puppy does not behave well and his owners are not happy. 
D) If the puppy is not trained and the puppy does not behave well, then his owners are not happy. 
A) If the puppy is not trained or the puppy does not behave well, then his owners are not happy. 
B) The puppy is not trained or the puppy does not behave well, and his owners are not happy. 
C) If the puppy is not trained then the puppy does not behave well and his owners are not happy. 
D) If the puppy is not trained and the puppy does not behave well, then his owners are not happy.

Question 13

Write a negation for the statement.
-Some athletes are musicians.

Accepted Answer

A) Some athletes are not musicians. 
B) No athlete is a musician. 
C) Not all athletes are musicians. 
D) All athletes are musicians. 
A) Some athletes are not musicians. 
B) No athlete is a musician. 
C) Not all athletes are musicians. 
D) All athletes are musicians.

Question 14

Use an Euler diagram to determine whether the argument is valid or invalid.
-Not all that glitters is gold. My ring glitters.
My ring is not gold.

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Write the converse, inverse, or contrapositive of the statement as requested.
-Love is blind. Contrapositive

Accepted Answer

A) If it is blind then it is not love. 
B) If it is blind then it is love. 
C) If it is not love, it is not blind. 
D) If it is not blind, then it is not love. 
A) If it is blind then it is not love. 
B) If it is blind then it is love. 
C) If it is not love, it is not blind. 
D) If it is not blind, then it is not love.

Question 17

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 and I eat too much, then I'll exercise.

Accepted Answer

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

Question 18

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

Accepted Answer

A) 
$\begin{array}{ccccc}
\mathrm{w} & \mathrm{t} & \mathrm{q} & \sim((\mathrm{w} \wedge \mathrm{t}) \vee \mathrm{q}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
B) 
$\begin{array}{cccc}
\mathrm{w} & \mathrm{t} & \mathrm{q} & \sim((\mathrm{w} \wedge \mathrm{t}) \vee \mathrm{q}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$ 
A) 
$\begin{array}{ccccc}
\mathrm{w} & \mathrm{t} & \mathrm{q} & \sim((\mathrm{w} \wedge \mathrm{t}) \vee \mathrm{q}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
B) 
$\begin{array}{cccc}
\mathrm{w} & \mathrm{t} & \mathrm{q} & \sim((\mathrm{w} \wedge \mathrm{t}) \vee \mathrm{q}) \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{F} & \mathrm{F}
\end{array}$

Question 19

Decide whether or not the following is a statement.
-0.2 = .02

Accepted Answer

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

Question 20

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement.
-$p \wedge q$

Accepted Answer

A) True 
 B)False

Label the pair of statements as either contrary or consistent. -Today is Friday. Tomorrow is Sunday.

Write the converse, inverse, or contrapositive of the statement as requested. -If I were young, I would be happy. Converse

The argument has a true conclusion. Identify the argument as valid or invalid. -8 is a real number. $\underline { \sqrt { 64 } \text {is a real number.} }$ 8 is $\sqrt { 64 }$ .

Decide whether the statement is compound. -Computers are very helpful to people.

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: $p \wedge q$

Write a negation for the statement. -Everyone is asleep.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -I'll leave when he arrives.

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 not good, I won't eat too much.

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, then I eat too much.

Determine whether the argument is valid or invalid. -Sam plays tennis or George is not a man. If George is not a man, then Betsy does not win the award. Betsy wins the award. Therefore, Sam does not play tennis.

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

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

Write a negation for the statement. -Some athletes are musicians.

Use an Euler diagram to determine whether the argument is valid or invalid. -Not all that glitters is gold. My ring glitters. My ring is not gold.

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

Write the converse, inverse, or contrapositive of the statement as requested. -Love is blind. Contrapositive

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 and I eat too much, then I'll exercise.

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

Decide whether or not the following is a statement. -0.2 = .02

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement. - $p \wedge q$

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