Question 1

Use a truth table to determine whether the argument is valid.
-$\begin{array} { c } 
\sim \mathrm { p } \rightarrow \mathrm { q } \
\frac { \sim q \rightarrow p } { p \vee q }
\end{array}$

Accepted Answer

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

Question 2

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument.
-All fish can dream. Any dead animal is unable to dream. All live animals have a heartbeat.

Accepted Answer

A) Any dead fish can dream. 
B) All live animals can dream. 
C) All fish have a heartbeat. 
D) Any dead animal has no heartbeat. 
A) Any dead fish can dream. 
B) All live animals can dream. 
C) All fish have a heartbeat. 
D) Any dead animal has no heartbeat.

Question 3

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

Accepted Answer

A) True 
 B)False

Question 4

Decide whether the statement is true or false.
-No rational number is not a whole number.

Accepted Answer

A) True 
 B)False

Question 5

Find the truth value of the statement.
-$6 \times 2 = 16 \text { if and only if } 9 + 7 = 16$

Accepted Answer

A) True 
 B)False

Question 6

Given p is true, q is true, and r is false, find the truth value of the statement.
-$\sim \mathrm { q } \wedge ( \mathrm { p } \wedge \sim \mathrm { r } )$

Accepted Answer

A) True 
 B)False

Question 7

Rewrite the statement in the form "if p, then q".
-$x = 6 \text { if } 2 x + 6 = 18$

Accepted Answer

A)  If $2 x + 6 = 18$, then $x = 6$. 
B)  If $x = 6$, then $2 x + 6 = 6$. 
C)  If $x \neq 6$, then $2 x + 6 = 18$. 
D)  If $2 x + 6 \neq 18$, then $x = 6$. 
A)  If $2 x + 6 = 18$, then $x = 6$. 
B)  If $x = 6$, then $2 x + 6 = 6$. 
C)  If $x \neq 6$, then $2 x + 6 = 18$. 
D)  If $2 x + 6 \neq 18$, then $x = 6$.

Question 8

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

Accepted Answer

A) True 
 B)False

Question 9

Tell whether the conditional statement is true or false.
-$( 5 = 5 ) \rightarrow ( 4 = 3 )$

Accepted Answer

A) True 
 B)False

Question 10

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

Accepted Answer

A) True 
 B)False

Question 11

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument.
-Students who watch television while doing homework jeopardize their grades. Students with grades in jeopardy get grounded. Being grounded includes being barred from watching television.

Accepted Answer

A) Students who are grounded watch TV while doing homework. 
B) Students who watch TV while doing homework will not be allowed to watch TV. 
C) Students who watch TV will be grounded. 
D) Students who watch TV will be barred from watching TV. 
A) Students who are grounded watch TV while doing homework. 
B) Students who watch TV while doing homework will not be allowed to watch TV. 
C) Students who watch TV will be grounded. 
D) Students who watch TV will be barred from watching TV.

Question 12

Determine whether the argument is valid or invalid.
-If Ann so wishes, then Bill will be the president. Manuel is a public defender or Bill will be the president. Manuel is not a public defender. Therefore, Ann does not so wish.

Accepted Answer

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

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

Use a truth table to determine whether the argument is valid.
-

Accepted Answer

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

Question 15

Decide whether the statement is true or false.
-$\text { For some real number } r , | 3 r - 15 | = 6 \text { and } r ^ { 2 } - 9 = 0 \text {. }$

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

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

Question 17

Write the converse, inverse, or contrapositive of the statement as requested.
-He who laughs last, laughs loudest. Inverse

Accepted Answer

A) If he laughs loudest, he laughs last. 
B) If he doesn't laugh loudest, he doesn't laugh last. 
C) If he doesn't laugh last, he doesn't laugh loudest. 
D) If he laughs last, he doesn't laugh loudest. 
A) If he laughs loudest, he laughs last. 
B) If he doesn't laugh loudest, he doesn't laugh last. 
C) If he doesn't laugh last, he doesn't laugh loudest. 
D) If he laughs last, he doesn't laugh loudest.

Question 18

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-All children like stuffed toys.

Accepted Answer

A) If children like it, then it's a stuffed toy. 
B) If it is a child, then it likes stuffed toys. 
C) All children like stuffed toys. 
D) If it is not a stuffed toy, then children like it. 
A) If children like it, then it's a stuffed toy. 
B) If it is a child, then it likes stuffed toys. 
C) All children like stuffed toys. 
D) If it is not a stuffed toy, then children like it.

Question 19

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary.
-I have not accepted anyone who is from out of town.

Accepted Answer

A) If I have not accepted a person, then they are from out of town. 
B) If the person is from out of town, I have not accepted them 
C) If the person is not from out of town, I have accepted them 
D) If I have accepted a person, then they are from out of town. 
A) If I have not accepted a person, then they are from out of town. 
B) If the person is from out of town, I have not accepted them 
C) If the person is not from out of town, I have accepted them 
D) If I have accepted a person, then they are from out of town.

Question 20

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

Accepted Answer

A) True 
 B)False

Use a truth table to determine whether the argument is valid. - \sim\rightarrow

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -All fish can dream. Any dead animal is unable to dream. All live animals have a heartbeat.

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

Decide whether the statement is true or false. -No rational number is not a whole number.

Find the truth value of the statement. - $6 \times 2 = 16 \text { if and only if } 9 + 7 = 16$

Given p is true, q is true, and r is false, find the truth value of the statement. - $\sim \mathrm { q } \wedge ( \mathrm { p } \wedge \sim \mathrm { r } )$

Rewrite the statement in the form "if p, then q". - $x = 6 \text { if } 2 x + 6 = 18$

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

Tell whether the conditional statement is true or false. - $( 5 = 5 ) \rightarrow ( 4 = 3 )$

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

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -Students who watch television while doing homework jeopardize their grades. Students with grades in jeopardy get grounded. Being grounded includes being barred from watching television.

Determine whether the argument is valid or invalid. -If Ann so wishes, then Bill will be the president. Manuel is a public defender or Bill will be the president. Manuel is not a public defender. Therefore, Ann does not so wish.

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

Use a truth table to determine whether the argument is valid. -

Decide whether the statement is true or false. - $\text { For some real number } r , | 3 r - 15 | = 6 \text { and } r ^ { 2 } - 9 = 0 \text {. }$

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

Write the converse, inverse, or contrapositive of the statement as requested. -He who laughs last, laughs loudest. Inverse

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -All children like stuffed toys.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -I have not accepted anyone who is from out of town.

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

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

Use a truth table to determine whether the argument is valid. - \sim\rightarrow

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -All fish can dream. Any dead animal is unable to dream. All live animals have a heartbeat.

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

Decide whether the statement is true or false. -No rational number is not a whole number.

Find the truth value of the statement. - 6×2=16 if and only if 9+7=166 \times 2 = 16 \text { if and only if } 9 + 7 = 166×2=16 if and only if 9+7=16

Given p is true, q is true, and r is false, find the truth value of the statement. - ∼q∧(p∧∼r)\sim \mathrm { q } \wedge ( \mathrm { p } \wedge \sim \mathrm { r } )∼q∧(p∧∼r)

Rewrite the statement in the form "if p, then q". - x=6 if 2x+6=18x = 6 \text { if } 2 x + 6 = 18x=6 if 2x+6=18

Let p represent a true statement and let q represent a false statement. Find the truth value of the given compound statement. - ∼[∼p∨(∼q∧p)]\sim [ \sim \mathrm { p } \vee ( \sim \mathrm { q } \wedge \mathrm { p } ) ]∼[∼p∨(∼q∧p)]

Tell whether the conditional statement is true or false. - (5=5)→(4=3)( 5 = 5 ) \rightarrow ( 4 = 3 )(5=5)→(4=3)

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

Use the method of writing each premise in symbols in order to write a conclusion that yields a valid argument. -Students who watch television while doing homework jeopardize their grades. Students with grades in jeopardy get grounded. Being grounded includes being barred from watching television.

Determine whether the argument is valid or invalid. -If Ann so wishes, then Bill will be the president. Manuel is a public defender or Bill will be the president. Manuel is not a public defender. Therefore, Ann does not so wish.

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

Use a truth table to determine whether the argument is valid. -

Decide whether the statement is true or false. - For some real number r,∣3r−15∣=6 and r2−9=0. \text { For some real number } r , | 3 r - 15 | = 6 \text { and } r ^ { 2 } - 9 = 0 \text {. } For some real number r,∣3r−15∣=6 and r2−9=0.

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

Write the converse, inverse, or contrapositive of the statement as requested. -He who laughs last, laughs loudest. Inverse

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -All children like stuffed toys.

Rewrite the statement using the if...then connective. Rearrange the wording or words as necessary. -I have not accepted anyone who is from out of town.

Given p is true, q is true, and r is false, find the truth value of the statement. - ∼q→(p∨r)\sim \mathrm { q } \rightarrow ( \mathrm { p } \vee \mathrm { r } )∼q→(p∨r)

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

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

Find the truth value of the statement. - $6 \times 2 = 16 \text { if and only if } 9 + 7 = 16$

Given p is true, q is true, and r is false, find the truth value of the statement. - $\sim \mathrm { q } \wedge ( \mathrm { p } \wedge \sim \mathrm { r } )$

Rewrite the statement in the form "if p, then q". - $x = 6 \text { if } 2 x + 6 = 18$

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

Tell whether the conditional statement is true or false. - $( 5 = 5 ) \rightarrow ( 4 = 3 )$

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

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

Decide whether the statement is true or false. - $\text { For some real number } r , | 3 r - 15 | = 6 \text { and } r ^ { 2 } - 9 = 0 \text {. }$

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

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