Question 1

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-If the food is good or if I eat too much, Iʹll exercise.

Accepted Answer

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

Question 2

Write an equivalent sentence for the statement.
-You do not give your rain coat to the doorman or he will give you a dirty look. (Hint: Use the fact That p → qis equivalent to ~p ∨ q.)

Accepted Answer

A)  You do not give your rain coat to the doorman and he will not give you a dirty look. 
B)  If you give your rain coat to the doorman, he will give you a dirty look. 
C)  You do not give your rain coat to the doorman and he will give you a dirty look. 
D)  If you give your rain coat to the doorman he will not give you a dirty look. 
A)  You do not give your rain coat to the doorman and he will not give you a dirty look. 
B)  If you give your rain coat to the doorman, he will give you a dirty look. 
C)  You do not give your rain coat to the doorman and he will give you a dirty look. 
D)  If you give your rain coat to the doorman he will not give you a dirty look.

Question 3

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
-The clown is not amusing.

Accepted Answer

A)  Compound; disjunction; $\vee$ 
B)  Simple statement, negation; $\sim$ 
C)  Simple statement 
D)  Compound; conjunction; $\wedge$ 
A)  Compound; disjunction; $\vee$ 
B)  Simple statement, negation; $\sim$ 
C)  Simple statement 
D)  Compound; conjunction; $\wedge$

Question 4

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement.
-A foot is equal to 16 inches, if and only if a meter is equal to 100 centimeters and a yard is equal to 5 feet.

Accepted Answer

A) True 
 B)False

Question 5

Write the compound statement in symbols. Then construct a truth table for the symbolic statement.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-If the food is not good, I won?t eat too much.

Accepted Answer

A) $\sim(r \rightarrow p)$
$\begin{array} { c c c } 
\mathrm { r } & \mathrm { p } & \sim ( \mathrm { r } \rightarrow \mathrm { p } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
B) $\sim(r \rightarrow p)$
$\begin{array} { c c c } 
\mathrm { r } & \mathrm { p } & \sim ( \mathrm { r } \rightarrow \mathrm { p } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
C) $\sim \mathbf{r} \rightarrow \sim \mathrm{p}$
$\begin{array} { c c c } 
\mathrm { r } & \mathrm { p } & \sim \mathrm { r } \rightarrow \sim \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
D) $\sim \mathrm{r} \rightarrow \sim \mathrm{P}$
$\begin{array} { c c c } 
\mathrm { r } & \mathrm { p } & \sim \mathrm { r } \rightarrow \sim \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
A) $\sim(r \rightarrow p)$
$\begin{array} { c c c } 
\mathrm { r } & \mathrm { p } & \sim ( \mathrm { r } \rightarrow \mathrm { p } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
B) $\sim(r \rightarrow p)$
$\begin{array} { c c c } 
\mathrm { r } & \mathrm { p } & \sim ( \mathrm { r } \rightarrow \mathrm { p } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
C) $\sim \mathbf{r} \rightarrow \sim \mathrm{p}$
$\begin{array} { c c c } 
\mathrm { r } & \mathrm { p } & \sim \mathrm { r } \rightarrow \sim \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
D) $\sim \mathrm{r} \rightarrow \sim \mathrm{P}$
$\begin{array} { c c c } 
\mathrm { r } & \mathrm { p } & \sim \mathrm { r } \rightarrow \sim \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

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

Write the compound statement in symbols. Then construct a truth table for the symbolic statement.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-The food is good and if I eat too much, then I?ll exercise.

Accepted Answer

A)  $(r \wedge p) \rightarrow q$
$\begin{array} { c c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { q } & \left( \mathrm { r } { \wedge } \mathrm { p } \right) \rightarrow \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
B) $r \wedge(p \rightarrow q)$
$\begin{array} { c c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { q } & \mathrm { r } \wedge ( \mathrm { p } \rightarrow \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
C) $(r \wedge p) \rightarrow q$
$\begin{array} { c c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { q } & \left( \mathrm { r }  { \wedge } \mathrm { p } \right) \rightarrow \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
D) $r \wedge(p \rightarrow q)$
$\begin{array} { c c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { q } & \mathrm { r } \wedge ( \mathrm { p } \rightarrow \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
A)  $(r \wedge p) \rightarrow q$
$\begin{array} { c c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { q } & \left( \mathrm { r } { \wedge } \mathrm { p } \right) \rightarrow \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
B) $r \wedge(p \rightarrow q)$
$\begin{array} { c c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { q } & \mathrm { r } \wedge ( \mathrm { p } \rightarrow \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
C) $(r \wedge p) \rightarrow q$
$\begin{array} { c c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { q } & \left( \mathrm { r }  { \wedge } \mathrm { p } \right) \rightarrow \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
D) $r \wedge(p \rightarrow q)$
$\begin{array} { c c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { q } & \mathrm { r } \wedge ( \mathrm { p } \rightarrow \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$

Question 8

Use the information given in the chart or graph to determine the truth values of the simple statements. Then determine the truth value of the compound statement given.
-  
The most common type of TV show watched by 13-29 year-olds is the sitcom, or 31% of 13-29 year-olds watch sports and 20% of 30-49 year-olds watch sports.

Accepted Answer

A) True 
 B)False

Question 9

Determine which, if any, of the three statements are equivalent.
-I. The raft flipped if and only if the guide misjudged the rapid or the crew fell overboard.
II. The crew fell overboard, or if the guide misjudged the rapid then the raft flipped.
III. If the guide misjudged the rapid, then the raft flipped or the crew fell overboard.

Accepted Answer

A)  I and II are equivalent 
B)  II and III are equivalent 
C)  I, II and III are equivalent 
D)  None are equivalent 
A)  I and II are equivalent 
B)  II and III are equivalent 
C)  I, II and III are equivalent 
D)  None are equivalent

Question 10

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-Iʹll exercise if I donʹt eat too much.

Accepted Answer

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

Question 11

Convert the compound statement into words.
-$\mathrm { p } =$ "Her name is Lisa."
$q =$ "She lives in Chicago."
$\sim \mathrm { p }$

Accepted Answer

A)  She does not live in Chicago. 
B)  Her name is not Lisa. 
C)  It is true her name is Lisa. 
D)  Her name is Lisa. 
A)  She does not live in Chicago. 
B)  Her name is not Lisa. 
C)  It is true her name is Lisa. 
D)  Her name is Lisa.

Question 12

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent.
-$$\sim ( \sim \mathrm { p } \rightarrow \mathrm { q } ) , \mathrm { p } \vee \sim \mathrm { q }$$

Accepted Answer

A)  Not equivalent 
B)  Equivalent 
A)  Not equivalent 
B)  Equivalent

Question 13

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
-The team leader has decided to take a vacation.

Accepted Answer

A)  Compound; conditional; $\rightarrow$ 
B)  Compound; negation; $\sim$ 
C)  Compound; conjunction; $\wedge$ 
D)  Simple statement 
A)  Compound; conditional; $\rightarrow$ 
B)  Compound; negation; $\sim$ 
C)  Compound; conjunction; $\wedge$ 
D)  Simple statement

Question 14

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these.
-$$\sim [ ( p - q ) \wedge ( q - p ) ] \rightarrow  \sim ( p \leftrightarrow q )$$

Accepted Answer

A)  Tautology 
B)  Implication 
C)  Self-contradiction 
D)  None of these 
A)  Tautology 
B)  Implication 
C)  Self-contradiction 
D)  None of these

Question 15

Construct a truth table for the statement.
-$\mathbf{r} \rightarrow \sim \mathrm{p}$

Accepted Answer

A) 
$\begin{array} { c c r } 
\mathrm { r } & \mathrm { p } & \mathrm { r } _\rightarrow \sim \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
B) 
$\begin{array} { l l l } 
\mathrm { r } & \mathrm { p } & \mathrm { r } _\rightarrow \sim \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
C) 
$\begin{array} { l l l } 
\mathrm { r } & \mathrm { p } & \mathrm { r } _ { \rightarrow } \sim \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
D) 
$\begin{array}{llr}
\mathrm{r} & \mathrm{P} & \mathrm{r}_\rightarrow \sim \mathrm{P} \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$ 
A) 
$\begin{array} { c c r } 
\mathrm { r } & \mathrm { p } & \mathrm { r } _\rightarrow \sim \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
B) 
$\begin{array} { l l l } 
\mathrm { r } & \mathrm { p } & \mathrm { r } _\rightarrow \sim \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
C) 
$\begin{array} { l l l } 
\mathrm { r } & \mathrm { p } & \mathrm { r } _ { \rightarrow } \sim \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
D) 
$\begin{array}{llr}
\mathrm{r} & \mathrm{P} & \mathrm{r}_\rightarrow \sim \mathrm{P} \
\hline \mathrm{T} & \mathrm{T} & \mathrm{F} \
\mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{T} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$

Question 16

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol.
-The animal is a mammal if and only if it nurses its young.

Accepted Answer

A)  Compound; disjunction; $\vee$ 
B)  Compound; biconditional; $\leftrightarrow$ 
C)  Compound; conditional; $\rightarrow$ 
D)  Compound; negation; $\sim$ 
A)  Compound; disjunction; $\vee$ 
B)  Compound; biconditional; $\leftrightarrow$ 
C)  Compound; conditional; $\rightarrow$ 
D)  Compound; negation; $\sim$

Question 17

Identify the standard form of the argument.
-$\begin{array} { l } 
\mathrm { p } \rightarrow \mathrm { q } \
\sim \mathrm { p } \
\hline\therefore \sim \mathrm { q }
\end{array}$

Accepted Answer

A)  Law of Syllogism 
B)  Law of Contraposition 
C)  Fallacy of the Converse 
D)  Fallacy of the Inverse 
A)  Law of Syllogism 
B)  Law of Contraposition 
C)  Fallacy of the Converse 
D)  Fallacy of the Inverse

Question 18

Write the compound statement in symbols.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-If I exercise, then I wonʹt eat too much.

Accepted Answer

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

Question 19

Construct a truth table for the statement.
-$\sim(\mathrm{s} \vee \mathrm{t}) \wedge \sim(\mathrm{t} \wedge \mathrm{s})$

Accepted Answer

A) 
$\begin{array} { l l c } 
\mathrm { s } & \mathrm { t } & \sim \left( \mathrm { s } _ { \vee } \mathrm { t } \right) \wedge \sim ( \mathrm { t } \wedge \mathrm { s } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
B) 
$\begin{array} { l l c } 
\mathrm { s } & \mathrm { t } & \sim ( \mathrm { s } \vee \mathrm { t } ) \wedge \sim ( \mathrm { t } \wedge \mathrm { s } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
C) 
$\begin{array} { c c c } 
\mathrm { s } & \mathrm { t } & \sim ( \mathrm { s } \vee \mathrm { t } ) \wedge \sim ( \mathrm { t } \wedge \mathrm { s } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
D) 
$\begin{array} { l l c } 
\mathrm { s } & \mathrm { t } & \sim ( \mathrm { s } \vee \mathrm { t } ) \wedge \sim ( \mathrm { t } \wedge \mathrm { s } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
A) 
$\begin{array} { l l c } 
\mathrm { s } & \mathrm { t } & \sim \left( \mathrm { s } _ { \vee } \mathrm { t } \right) \wedge \sim ( \mathrm { t } \wedge \mathrm { s } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
B) 
$\begin{array} { l l c } 
\mathrm { s } & \mathrm { t } & \sim ( \mathrm { s } \vee \mathrm { t } ) \wedge \sim ( \mathrm { t } \wedge \mathrm { s } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
C) 
$\begin{array} { c c c } 
\mathrm { s } & \mathrm { t } & \sim ( \mathrm { s } \vee \mathrm { t } ) \wedge \sim ( \mathrm { t } \wedge \mathrm { s } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
D) 
$\begin{array} { l l c } 
\mathrm { s } & \mathrm { t } & \sim ( \mathrm { s } \vee \mathrm { t } ) \wedge \sim ( \mathrm { t } \wedge \mathrm { s } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$

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

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If the food is good or if I eat too much, Iʹll exercise.

Write an equivalent sentence for the statement. -You do not give your rain coat to the doorman or he will give you a dirty look. (Hint: Use the fact That p → qis equivalent to ~p ∨ q.)

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. -The clown is not amusing.

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement. -A foot is equal to 16 inches, if and only if a meter is equal to 100 centimeters and a yard is equal to 5 feet.

Write the compound statement in symbols. Then construct a truth table for the symbolic statement. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If the food is not good, I won?t eat too much.

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

Write the compound statement in symbols. Then construct a truth table for the symbolic statement. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -The food is good and if I eat too much, then I?ll exercise.

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -Iʹll exercise if I donʹt eat too much.

Convert the compound statement into words. - $\mathrm { p } =$ "Her name is Lisa." $q =$ "She lives in Chicago." $\sim \mathrm { p }$

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent. - $\sim ( \sim \mathrm { p } \rightarrow \mathrm { q } ) , \mathrm { p } \vee \sim \mathrm { q }$

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. -The team leader has decided to take a vacation.

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. - $\sim [ ( p - q ) \wedge ( q - p ) ] \rightarrow \sim ( p \leftrightarrow q )$

Construct a truth table for the statement. - $\mathbf{r} \rightarrow \sim \mathrm{p}$

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. -The animal is a mammal if and only if it nurses its young.

Identify the standard form of the argument. - \rightarrow \sim \therefore\sim

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If I exercise, then I wonʹt eat too much.

Construct a truth table for the statement. - $\sim(\mathrm{s} \vee \mathrm{t}) \wedge \sim(\mathrm{t} \wedge \mathrm{s})$

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

Critical Thinking Skills

Sets

Systems of Numeration

Number Theory and the Real Number System

Algebra, Graphs, and Functions

The Metric System

Geometry

Consumer Mathematics

Probability

Voting and Apportionment

Filters

Exam 3: Logic

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If the food is good or if I eat too much, Iʹll exercise.

Write an equivalent sentence for the statement. -You do not give your rain coat to the doorman or he will give you a dirty look. (Hint: Use the fact That p → qis equivalent to ~p ∨ q.)

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. -The clown is not amusing.

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement. -A foot is equal to 16 inches, if and only if a meter is equal to 100 centimeters and a yard is equal to 5 feet.

Write the compound statement in symbols. Then construct a truth table for the symbolic statement. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If the food is not good, I won?t eat too much.

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)

Write the compound statement in symbols. Then construct a truth table for the symbolic statement. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -The food is good and if I eat too much, then I?ll exercise.

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -Iʹll exercise if I donʹt eat too much.

Convert the compound statement into words. - p=\mathrm { p } =p= "Her name is Lisa." q=q =q= "She lives in Chicago." ∼p\sim \mathrm { p }∼p

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent. - ∼(∼p→q),p∨∼q\sim ( \sim \mathrm { p } \rightarrow \mathrm { q } ) , \mathrm { p } \vee \sim \mathrm { q }∼(∼p→q),p∨∼q

Indicate whether the statement is a simple or a compound statement. If it is a compound statement, indicate whether it is a negation, conjunction, disjunction, conditional, or biconditional by using both the word and its appropriate symbol. -The team leader has decided to take a vacation.

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. - ∼[(p−q)∧(q−p)]→∼(p↔q)\sim [ ( p - q ) \wedge ( q - p ) ] \rightarrow \sim ( p \leftrightarrow q )∼[(p−q)∧(q−p)]→∼(p↔q)

Construct a truth table for the statement. - r→∼p\mathbf{r} \rightarrow \sim \mathrm{p}r→∼p

Identify the standard form of the argument. - \rightarrow \sim \therefore\sim

Write the compound statement in symbols. Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ -If I exercise, then I wonʹt eat too much.

Construct a truth table for the statement. - ∼(s∨t)∧∼(t∧s)\sim(\mathrm{s} \vee \mathrm{t}) \wedge \sim(\mathrm{t} \wedge \mathrm{s})∼(s∨t)∧∼(t∧s)

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)

Critical Thinking Skills

Sets

Systems of Numeration

Number Theory and the Real Number System

Algebra, Graphs, and Functions

The Metric System

Geometry

Consumer Mathematics

Probability

Voting and Apportionment

Filters

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

Convert the compound statement into words. - $\mathrm { p } =$ "Her name is Lisa." $q =$ "She lives in Chicago." $\sim \mathrm { p }$

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent. - $\sim ( \sim \mathrm { p } \rightarrow \mathrm { q } ) , \mathrm { p } \vee \sim \mathrm { q }$

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. - $\sim [ ( p - q ) \wedge ( q - p ) ] \rightarrow \sim ( p \leftrightarrow q )$

Construct a truth table for the statement. - $\mathbf{r} \rightarrow \sim \mathrm{p}$

Construct a truth table for the statement. - $\sim(\mathrm{s} \vee \mathrm{t}) \wedge \sim(\mathrm{t} \wedge \mathrm{s})$

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