Question 1

Convert the compound statement into words.
-$$\begin{array} { l } 
\mathrm { p } = \text { "The food tastes delicious." } \
\mathrm { q } = \text { "We eat a lot." } \
\mathrm { r } = \text { "Nobody has dessert." } \
\sim \mathrm { q } \vee ( \mathrm { p } \wedge \mathrm { r } )
\end{array}$$

Accepted Answer

A)  We do not eat a lot and the food tastes delicious and nobody has dessert. 
B)  We eat a lot or the food tastes delicious and nobody has dessert. 
C)  We do not eat a lot or the food tastes delicious or nobody has dessert. 
D)  We do not eat a lot or the food tastes delicious and nobody has dessert. 
A)  We do not eat a lot and the food tastes delicious and nobody has dessert. 
B)  We eat a lot or the food tastes delicious and nobody has dessert. 
C)  We do not eat a lot or the food tastes delicious or nobody has dessert. 
D)  We do not eat a lot or the food tastes delicious and nobody has dessert.

Question 2

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement.
-$$\text { If } 7  4 \text {, then } 9 < 10$$

Accepted Answer

A) True 
 B)False

Question 3

Determine the truth value for the simple statement. Then use these truth values to determine the truth value of the compound statement. Use the chart or graph when provided.
-9 + 6 = 20 - 5 and 48 ÷ 4 = 4 ∙ 3

Accepted Answer

A) True 
 B)False

Question 4

Use truth tables to test the validity of the argument.
-$\begin{array} { l } 
\mathrm { p } \rightarrow \sim \mathrm { q } \
 \mathrm { q } \sim \sim \mathrm { p } \
\hline  \therefore   \mathrm { p } \vee \mathrm { q } 
\end{array}$

Accepted Answer

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

Question 5

Determine which, if any, of the three statements are equivalent.
-I. If tomorrow is not Monday, then today is not Sunday.
II. Today is not Sunday and tomorrow is not Monday.
III. It is not the case that today is Sunday and tomorrow is Monday.

Accepted Answer

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

Question 6

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols.
-Neither Jim plays football nor Michael plays basketball.

Accepted Answer

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

Question 7

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement.
-$$\sim ( \mathrm { p } \wedge \mathrm { q } ) \wedge ( \mathrm { r } \vee \sim \mathrm { q } )$$

Accepted Answer

A) True 
 B)False

Question 8

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement.
-One dollar has the same value as 5 dimes and one quarter has the same value as 25 pennies, or one dime has the same value as 5 nickels.

Accepted Answer

A) True 
 B)False

Question 9

Translate the statement into symbols then construct a truth table.
-$ \mathrm{p}= $ The doctor prescribed medicine.
$ \mathrm{q}= $ The patient has recovered.
The doctor did not prescribe medicine but the patient recovered.

Accepted Answer

A) 
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim \mathrm { p } \vee \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
B) 
$\begin{array} { c c r } 
\mathrm { p } & \mathrm { q } & \sim \mathrm { p } \wedge \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
C) 
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim \mathrm { p } \wedge \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
D) 
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim \mathrm { p } \vee \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
A) 
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim \mathrm { p } \vee \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
B) 
$\begin{array} { c c r } 
\mathrm { p } & \mathrm { q } & \sim \mathrm { p } \wedge \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
C) 
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim \mathrm { p } \wedge \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
D) 
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim \mathrm { p } \vee \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$

Question 10

Determine which, if any, of the three statements are equivalent.
-I. If the garden needs watering, then the garden needs weeding or the garden is not lovely.
II. The garden needs watering, and it is false that the garden does not need weeding and the Garden is not lovely.
III. The garden needs watering, and the garden needs weeding or the garden is lovely.

Accepted Answer

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

Question 11

Translate the statement into symbols then construct a truth table.
-$ \mathrm{p}= $ The garden contains sunflowers.
$ \mathrm{q}= $ The fence is painted white.
$ \mathrm{r}= $ The lawnmower is electric.
The garden contains sunflowers or the fence is painted white, or the lawnmower is electric.

Accepted Answer

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

Question 12

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 not good, I wonʹt eat too much.

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Select letters to represent the simple statements and write each statement symbolically by using parentheses then indicate whether the statement is a negation, conjunction, disjunction, conditional, or biconditional.
-If a number is divisible by 3 and the number is not divisible by 2 then the number is not divisible By 6.

Accepted Answer

A)  $\mathrm { p } \wedge ( \sim \mathrm { q } \rightarrow \sim \mathrm { r } )$; conjunction 
B)  $\mathrm { p } \vee ( \sim \mathrm { q } \rightarrow \sim \mathrm { r } )$; disjunction 
C)  $( \mathrm { p } \wedge \sim \mathrm { q } ) \leftrightarrow ( \sim \mathrm { r } )$; biconditional 
D)  $( \mathrm { p } \wedge \sim \mathrm { q } ) \rightarrow ( \sim \mathrm { r } )$; conditional 
A)  $\mathrm { p } \wedge ( \sim \mathrm { q } \rightarrow \sim \mathrm { r } )$; conjunction 
B)  $\mathrm { p } \vee ( \sim \mathrm { q } \rightarrow \sim \mathrm { r } )$; disjunction 
C)  $( \mathrm { p } \wedge \sim \mathrm { q } ) \leftrightarrow ( \sim \mathrm { r } )$; biconditional 
D)  $( \mathrm { p } \wedge \sim \mathrm { q } ) \rightarrow ( \sim \mathrm { r } )$; conditional

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent.
-$ (q \rightarrow p) \wedge(p \rightarrow q),(q \leftrightarrow p) $

Accepted Answer

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

Question 17

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.
-  
36% of 30-49 year-olds watch sitcoms if and only if 6% of 13-29 year-olds watch news and younger viewers watch sports less often than older viewers.

Accepted Answer

A) True 
 B)False

Question 18

Write the indicated statement. Use De Morgan's Laws if necessary.
-If $x = 7$, then $x ^ { 2 } = 49$
Converse

Accepted Answer

A)  If $x ^ { 2 } \neq 49$, then $x \neq 7$. 
B)  If $x ^ { 2 } = 49$, then $x = 7$ 
C)  If $x \neq 7$, then $x ^ { 2 } \neq 49$. 
D)  If $x = 7$, then $x ^ { 2 } = 49$. 
A)  If $x ^ { 2 } \neq 49$, then $x \neq 7$. 
B)  If $x ^ { 2 } = 49$, then $x = 7$ 
C)  If $x \neq 7$, then $x ^ { 2 } \neq 49$. 
D)  If $x = 7$, then $x ^ { 2 } = 49$.

Question 19

Write the indicated statement. Use De Morgan's Laws if necessary.
-If I pass, Iʹll party.
Contrapositive

Accepted Answer

A)  If I party, then I passed. 
B)  If I donʹt party, I didnʹt pass. 
C)  If I donʹt pass, I wonʹt party. 
D)  Iʹll party if I pass. 
A)  If I party, then I passed. 
B)  If I donʹt party, I didnʹt pass. 
C)  If I donʹt pass, I wonʹt party. 
D)  Iʹll party if I pass.

Question 20

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement.
-$$\sim [ \sim p \wedge ( \sim q \vee p ) ]$$

Accepted Answer

A) True 
 B)False

Convert the compound statement into words. - = "The food tastes delicious." = "We eat a lot." = "Nobody has dessert." \sim\vee(\wedge)

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement. - $\text { If } 7 < 10 \text { and } 8 > 4 \text {, then } 9 < 10$

Determine the truth value for the simple statement. Then use these truth values to determine the truth value of the compound statement. Use the chart or graph when provided. -9 + 6 = 20 - 5 and 48 ÷ 4 = 4 ∙ 3

Use truth tables to test the validity of the argument. - \rightarrow\sim \sim\sim \therefore\vee

Determine which, if any, of the three statements are equivalent. -I. If tomorrow is not Monday, then today is not Sunday. II. Today is not Sunday and tomorrow is not Monday. III. It is not the case that today is Sunday and tomorrow is Monday.

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Neither Jim plays football nor Michael plays basketball.

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - $\sim ( \mathrm { p } \wedge \mathrm { q } ) \wedge ( \mathrm { r } \vee \sim \mathrm { q } )$

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement. -One dollar has the same value as 5 dimes and one quarter has the same value as 25 pennies, or one dime has the same value as 5 nickels.

Translate the statement into symbols then construct a truth table. - $\mathrm{p}=$ The doctor prescribed medicine. $\mathrm{q}=$ The patient has recovered. The doctor did not prescribe medicine but the patient recovered.

Translate the statement into symbols then construct a truth table. - $\mathrm{p}=$ The garden contains sunflowers. $\mathrm{q}=$ The fence is painted white. $\mathrm{r}=$ The lawnmower is electric. The garden contains sunflowers or the fence is painted white, or the lawnmower is electric.

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 not good, I wonʹt eat too much.

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

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

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent. - $(q \rightarrow p) \wedge(p \rightarrow q),(q \leftrightarrow p)$

Write the indicated statement. Use De Morgan's Laws if necessary. -If $x = 7$ , then $x ^ { 2 } = 49$ Converse

Write the indicated statement. Use De Morgan's Laws if necessary. -If I pass, Iʹll party. Contrapositive

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - $\sim [ \sim p \wedge ( \sim q \vee p ) ]$

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

Convert the compound statement into words. - = "The food tastes delicious." = "We eat a lot." = "Nobody has dessert." \sim\vee(\wedge)

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement. - If 7<10 and 8>4, then 9<10\text { If } 7 < 10 \text { and } 8 > 4 \text {, then } 9 < 10 If 7<10 and 8>4, then 9<10

Determine the truth value for the simple statement. Then use these truth values to determine the truth value of the compound statement. Use the chart or graph when provided. -9 + 6 = 20 - 5 and 48 ÷ 4 = 4 ∙ 3

Use truth tables to test the validity of the argument. - \rightarrow\sim \sim\sim \therefore\vee

Determine which, if any, of the three statements are equivalent. -I. If tomorrow is not Monday, then today is not Sunday. II. Today is not Sunday and tomorrow is not Monday. III. It is not the case that today is Sunday and tomorrow is Monday.

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Neither Jim plays football nor Michael plays basketball.

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - ∼(p∧q)∧(r∨∼q)\sim ( \mathrm { p } \wedge \mathrm { q } ) \wedge ( \mathrm { r } \vee \sim \mathrm { q } )∼(p∧q)∧(r∨∼q)

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement. -One dollar has the same value as 5 dimes and one quarter has the same value as 25 pennies, or one dime has the same value as 5 nickels.

Translate the statement into symbols then construct a truth table. - p= \mathrm{p}= p= The doctor prescribed medicine. q= \mathrm{q}= q= The patient has recovered. The doctor did not prescribe medicine but the patient recovered.

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 not good, I wonʹt eat too much.

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

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 ) \leftrightarrow \sim r(∼p∧q)↔∼r

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent. - (q→p)∧(p→q),(q↔p) (q \rightarrow p) \wedge(p \rightarrow q),(q \leftrightarrow p) (q→p)∧(p→q),(q↔p)

Write the indicated statement. Use De Morgan's Laws if necessary. -If x=7x = 7x=7 , then x2=49x ^ { 2 } = 49x2=49 Converse

Write the indicated statement. Use De Morgan's Laws if necessary. -If I pass, Iʹll party. Contrapositive

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - ∼[∼p∧(∼q∨p)]\sim [ \sim p \wedge ( \sim q \vee p ) ]∼[∼p∧(∼q∨p)]

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

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement. - $\text { If } 7 < 10 \text { and } 8 > 4 \text {, then } 9 < 10$

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - $\sim ( \mathrm { p } \wedge \mathrm { q } ) \wedge ( \mathrm { r } \vee \sim \mathrm { q } )$

Translate the statement into symbols then construct a truth table. - $\mathrm{p}=$ The doctor prescribed medicine. $\mathrm{q}=$ The patient has recovered. The doctor did not prescribe medicine but the patient recovered.

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

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

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent. - $(q \rightarrow p) \wedge(p \rightarrow q),(q \leftrightarrow p)$

Write the indicated statement. Use De Morgan's Laws if necessary. -If $x = 7$ , then $x ^ { 2 } = 49$ Converse

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. - $\sim [ \sim p \wedge ( \sim q \vee p ) ]$