Question 1

Label the pair of statements as either contrary or consistent.
-This number is greater than 20. This number is negative.

Accepted Answer

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

Question 2

Write the converse, inverse, or contrapositive of the statement as requested.
-If you like me, then I like you. Converse

Accepted Answer

A) I don't like you if you don't like me. 
B) If I like you, then you like me. 
C) I like you if you don't like me. 
D) If you don't like me, I don't like you. 
A) I don't like you if you don't like me. 
B) If I like you, then you like me. 
C) I like you if you don't like me. 
D) If you don't like me, I don't like you.

Question 3

Solve the logic puzzle by using a grid.
-Five students, Cynthia, Paulene, Chris, Mary and Janet got colored paper. No two had the same color. The six colors were: red, orange, white, black, yellow and green. Cynthia got a bright color.
Janet and Paulene got similar colors. Chris didn't get red. Mary didn't get green. Neither Chris nor
Paulene got orange. Cynthia and Paulene's colors combine to make Janet's color. Mary got the
Darkest color. Chris did not get white. Match students and colors.

Accepted Answer

A) Cynthia - white; Paulene - red; Chris - green; Mary - black; Janet - orange 
B) Cynthia - yellow; Paulene - red; Chris - white; Mary - black; Janet - orange 
C) Cynthia - yellow; Paulene - red; Chris - green; Mary - orange; Janet - black 
D) Cynthia - yellow; Paulene - red; Chris - green; Mary - black; Janet - orange 
A) Cynthia - white; Paulene - red; Chris - green; Mary - black; Janet - orange 
B) Cynthia - yellow; Paulene - red; Chris - white; Mary - black; Janet - orange 
C) Cynthia - yellow; Paulene - red; Chris - green; Mary - orange; Janet - black 
D) Cynthia - yellow; Paulene - red; Chris - green; Mary - black; Janet - orange

Question 4

Tell whether the conditional statement is true or false.
-Here T represents a true statement. $\mathrm { T } \rightarrow ( 5 < 3 )$

Accepted Answer

A) True 
 B)False

Question 5

The argument has a true conclusion. Identify the argument as valid or invalid.
-All soda pops are carbonated.
$\underline { \text {All diet colas are soda pops.} }$
All diet colas are carbonated.

Accepted Answer

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

Question 6

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 suit needs cleaning, you drop it off this afternoon.

Accepted Answer

A) Your suit does not need cleaning or you do not drop it off this afternoon. 
B) Your suit needs cleaning and you do not drop it off this afternoon. 
C) Your suit does not need cleaning so you do not drop it off this afternoon. 
D) Your suit does not need cleaning or you drop it off this afternoon. 
A) Your suit does not need cleaning or you do not drop it off this afternoon. 
B) Your suit needs cleaning and you do not drop it off this afternoon. 
C) Your suit does not need cleaning so you do not drop it off this afternoon. 
D) Your suit does not need cleaning or you drop it off this afternoon.

Question 7

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

Accepted Answer

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

Question 8

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-Cats chase mice.

Accepted Answer

A) Cats chase mice. 
B) If it is a cat, then it chases mice. 
C) If a cat is chasing it, then it is a mouse. 
D) If cats chase, then they chase mice. 
A) Cats chase mice. 
B) If it is a cat, then it chases mice. 
C) If a cat is chasing it, then it is a mouse. 
D) If cats chase, then they chase mice.

Question 9

Solve the problem.
-Given that $( p \wedge q ) \vee \sim q$ is false, what can you conclude about the truth values of $p$ and $q$ ?

Accepted Answer

A)  $p$ is false and $q$ is true 
B)  $p$ is false, $q$ can be either true or false 
C)  At least one of $p$ and $q$ is true 
D)  $p$ and $q$ can have any truth values 
A)  $p$ is false and $q$ is true 
B)  $p$ is false, $q$ can be either true or false 
C)  At least one of $p$ and $q$ is true 
D)  $p$ and $q$ can have any truth values

Question 10

Use an Euler diagram to determine whether the argument is valid or invalid.
-All painters use paint.
All painters use brushes.
$\underline { \text {Some people who use paint are teachers.} }$
Some painters are teachers.

Accepted Answer

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

Question 11

Determine whether the argument is valid or invalid.
-Michael Bolton is a hunk or Madonna cannot sing. If Madonna cannot sing, then Cigar does not win the Triple Crown. Cigar wins the Triple Crown. Therefore, Michael Bolton is not a hunk.

Accepted Answer

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

Question 12

Rewrite the statement in the form "if p, then q".
-$| \mathrm { y } | = 11$ only if $\mathrm { y } = \pm 11$.

Accepted Answer

A)  If $| y | \neq 11$, then $y = \pm 11$. 
B)  If $y \neq \pm 11$, then $| y | = 11$. 
C)  If $| y | = 11$, then $y = \pm 11$. 
D)  If $y = \pm 11$, then $| y | = 11$. 
A)  If $| y | \neq 11$, then $y = \pm 11$. 
B)  If $y \neq \pm 11$, then $| y | = 11$. 
C)  If $| y | = 11$, then $y = \pm 11$. 
D)  If $y = \pm 11$, then $| y | = 11$.

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

Determine whether the argument is valid or invalid.
-If I hear that poem, it reminds me of my mother. If I get sentimental, then it does not remind me of my mother. I get sentimental. Therefore, I don't hear that poem.

Accepted Answer

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

Question 15

Write a logical statement representing the following circuit. Simplify when possible.
-

Accepted Answer

The answer of Write a logical statement representing the following...

Question 16

Use an Euler diagram to determine whether the argument is valid or invalid.
-All cats like fish.
$\underline { \text { Henry does not like fish. } }$
Henry is not a cat.

Accepted Answer

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

Question 17

Decide whether or not the following is a statement.
-This test is too hard.

Accepted Answer

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

Question 18

Decide whether the statement is true or false.
-$\text { For some real number } x , x > 8 \text { and } | x | < 8 \text {. }$

Accepted Answer

A) True 
 B)False

Question 19

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-No turkeys like Thanksgiving.

Accepted Answer

A) If it is a turkey, then it doesn't like Thanksgiving. 
B) If it is not Thanksgiving, then no turkeys like it. 
C) If it is Thanksgiving, then turkeys like it. 
D) If it is not a turkey, then it likes Thanksgiving. 
A) If it is a turkey, then it doesn't like Thanksgiving. 
B) If it is not Thanksgiving, then no turkeys like it. 
C) If it is Thanksgiving, then turkeys like it. 
D) If it is not a turkey, then it likes Thanksgiving.

Question 20

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument.
-Smiling people are happy. Alert people are not happy. Careful drivers are alert. Careless drivers have accidents.

Accepted Answer

A) Careful drivers are happy. 
B) People who smile are alert. 
C) People who smile have accidents. 
D) Careful drivers have accidents. 
A) Careful drivers are happy. 
B) People who smile are alert. 
C) People who smile have accidents. 
D) Careful drivers have accidents.

Label the pair of statements as either contrary or consistent. -This number is greater than 20. This number is negative.

Write the converse, inverse, or contrapositive of the statement as requested. -If you like me, then I like you. Converse

Tell whether the conditional statement is true or false. -Here T represents a true statement. $\mathrm { T } \rightarrow ( 5 < 3 )$

The argument has a true conclusion. Identify the argument as valid or invalid. -All soda pops are carbonated. $\underline { \text {All diet colas are soda pops.} }$ All diet colas are carbonated.

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 suit needs cleaning, you drop it off this afternoon.

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

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -Cats chase mice.

Solve the problem. -Given that $( p \wedge q ) \vee \sim q$ is false, what can you conclude about the truth values of $p$ and $q$ ?

Use an Euler diagram to determine whether the argument is valid or invalid. -All painters use paint. All painters use brushes. $\underline { \text {Some people who use paint are teachers.} }$ Some painters are teachers.

Determine whether the argument is valid or invalid. -Michael Bolton is a hunk or Madonna cannot sing. If Madonna cannot sing, then Cigar does not win the Triple Crown. Cigar wins the Triple Crown. Therefore, Michael Bolton is not a hunk.

Rewrite the statement in the form "if p, then q". - $| \mathrm { y } | = 11$ only if $\mathrm { y } = \pm 11$ .

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

Determine whether the argument is valid or invalid. -If I hear that poem, it reminds me of my mother. If I get sentimental, then it does not remind me of my mother. I get sentimental. Therefore, I don't hear that poem.

Write a logical statement representing the following circuit. Simplify when possible. -

Use an Euler diagram to determine whether the argument is valid or invalid. -All cats like fish. $\underline { \text { Henry does not like fish. } }$ Henry is not a cat.

Decide whether or not the following is a statement. -This test is too hard.

Decide whether the statement is true or false. - $\text { For some real number } x , x > 8 \text { and } | x | < 8 \text {. }$

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -No turkeys like Thanksgiving.

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -Smiling people are happy. Alert people are not happy. Careful drivers are alert. Careless drivers have accidents.

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

Label the pair of statements as either contrary or consistent. -This number is greater than 20. This number is negative.

Write the converse, inverse, or contrapositive of the statement as requested. -If you like me, then I like you. Converse

Tell whether the conditional statement is true or false. -Here T represents a true statement. T→(5<3)\mathrm { T } \rightarrow ( 5 < 3 )T→(5<3)

The argument has a true conclusion. Identify the argument as valid or invalid. -All soda pops are carbonated. All diet colas are soda pops.‾\underline { \text {All diet colas are soda pops.} }All diet colas are soda pops.​ All diet colas are carbonated.

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

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -Cats chase mice.

Solve the problem. -Given that (p∧q)∨∼q( p \wedge q ) \vee \sim q(p∧q)∨∼q is false, what can you conclude about the truth values of ppp and qqq ?

Determine whether the argument is valid or invalid. -Michael Bolton is a hunk or Madonna cannot sing. If Madonna cannot sing, then Cigar does not win the Triple Crown. Cigar wins the Triple Crown. Therefore, Michael Bolton is not a hunk.

Rewrite the statement in the form "if p, then q". - ∣y∣=11| \mathrm { y } | = 11∣y∣=11 only if y=±11\mathrm { y } = \pm 11y=±11 .

When using a truth table, the statement ∼(∼q)\sim ( \sim \mathrm { q } )∼(∼q) is equivalent to q\mathrm { q }q .

Determine whether the argument is valid or invalid. -If I hear that poem, it reminds me of my mother. If I get sentimental, then it does not remind me of my mother. I get sentimental. Therefore, I don't hear that poem.

Write a logical statement representing the following circuit. Simplify when possible. -

Use an Euler diagram to determine whether the argument is valid or invalid. -All cats like fish. Henry does not like fish. ‾\underline { \text { Henry does not like fish. } } Henry does not like fish. ​ Henry is not a cat.

Decide whether or not the following is a statement. -This test is too hard.

Decide whether the statement is true or false. - For some real number x,x>8 and ∣x∣<8. \text { For some real number } x , x > 8 \text { and } | x | < 8 \text {. } For some real number x,x>8 and ∣x∣<8.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -No turkeys like Thanksgiving.

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -Smiling people are happy. Alert people are not happy. Careful drivers are alert. Careless drivers have accidents.

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

Tell whether the conditional statement is true or false. -Here T represents a true statement. $\mathrm { T } \rightarrow ( 5 < 3 )$

The argument has a true conclusion. Identify the argument as valid or invalid. -All soda pops are carbonated. $\underline { \text {All diet colas are soda pops.} }$ All diet colas are carbonated.

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

Solve the problem. -Given that $( p \wedge q ) \vee \sim q$ is false, what can you conclude about the truth values of $p$ and $q$ ?

Rewrite the statement in the form "if p, then q". - $| \mathrm { y } | = 11$ only if $\mathrm { y } = \pm 11$ .

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

Use an Euler diagram to determine whether the argument is valid or invalid. -All cats like fish. $\underline { \text { Henry does not like fish. } }$ Henry is not a cat.

Decide whether the statement is true or false. - $\text { For some real number } x , x > 8 \text { and } | x | < 8 \text {. }$