Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Translate the statement into symbols then construct a truth table.
-$ \mathrm{p}= $ Parker will work in an office.
$ \mathrm{q} $ = Parker will work as a forest ranger.
$ \mathrm{r}= $ Parker will work as a landscape architect.
Parker will not work in an office, but he will work as a forest ranger or a landscape architect.

Accepted Answer

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

Question 4

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 apartment is rented or it is available.

Accepted Answer

A)  Compound; conjunction; $\wedge$ 
B)  Compound; disjunction; $\vee$ 
C)  Compound; biconditional; $\leftrightarrow$ 
D)  Compound; conditional; $\rightarrow$ 
A)  Compound; conjunction; $\wedge$ 
B)  Compound; disjunction; $\vee$ 
C)  Compound; biconditional; $\leftrightarrow$ 
D)  Compound; conditional; $\rightarrow$

Question 5

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

Accepted Answer

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

Question 6

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.
-$$\begin{array}{l}
\text { Planet X }\
\begin{array} { c c c c } 
\hline \bullet & \text { Moon 1 } & & \
\text { o } & \text { Moon 2 } & \text { Diameter of moons: } & \text { May have: } \
\text { o } & \text { Moon 3 } & \text { o } 3 - 8 \mathrm {~km} & \text { o water ice } \
\circ & \text { Moon 4 } & \circ 9 - 14 \mathrm {~km} &\bullet \text {  atmosphere } \
0 & \text { Moon 5 } & \bullet 15 - 24 \mathrm {~km} & \text { o both }
\end{array}
\end{array}$$ 
Moon 1 has a smaller diameter than Moon 3 and Moon 5 may have water ice, if and only if Moon 2 may have both water ice and an atmosphere.

Accepted Answer

A) True 
 B)False

Question 7

Write an equivalent sentence for the statement.
-If the box is in the mail, then it should be here by tomorrow. (Hint: Use the fact that p → q is Equivalent to ~p ∨ q.)

Accepted Answer

A)  If the box is in the mail, then it should not be here by tomorrow. 
B)  The box is not in the mail or it should be here by tomorrow. 
C)  The box is in the mail so it should be here by tomorrow. 
D)  The box is not in the mail and it should not be here by tomorrow. 
A)  If the box is in the mail, then it should not be here by tomorrow. 
B)  The box is not in the mail or it should be here by tomorrow. 
C)  The box is in the mail so it should be here by tomorrow. 
D)  The box is not in the mail and it should not be here by tomorrow.

Question 8

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

Accepted Answer

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

Question 9

Write the indicated statement. Use De Morgan's Laws if necessary.
-If you like me, then I like you.
Converse

Accepted Answer

A)  I like you if you donʹt like me. 
B)  If you donʹt like me, I donʹt like you. 
C)  I donʹt like you if you donʹt like me. 
D)  If I like you, then you like me. 
A)  I like you if you donʹt like me. 
B)  If you donʹt like me, I donʹt like you. 
C)  I donʹt like you if you donʹt like me. 
D)  If I like you, then you like me.

Question 10

Determine which, if any, of the three statements are equivalent.
-I. Gasoline costs $1.99 per gallon if and only if you live in Cook County.
II. You do not live in Cook County and gasoline does not cost $1.99 per gallon.
III. If you do not live in Cook County then gasoline does not cost $1.99 per gallon and if gasoline Does not cost $1.99 per gallon then you do not live in Cook County.

Accepted Answer

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

Question 11

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

Accepted Answer

A)  The puppy behaves well and his owners are happy. 
B)  It is not the case that if the puppy behaves well then his owners are happy. 
C)  The puppy behaves well or his owners are happy. 
D)  If the puppy does not behave well then his owners are not happy. 
A)  The puppy behaves well and his owners are happy. 
B)  It is not the case that if the puppy behaves well then his owners are happy. 
C)  The puppy behaves well or his owners are happy. 
D)  If the puppy does not behave well then his owners are not happy.

Question 12

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

Accepted Answer

A) True 
 B)False

Question 13

Write an equivalent sentence for the statement.
-If you canʹt take the heat, stay out of the sun. (Hint: Use the fact that p → q is equivalent to ~p ∨ q.)

Accepted Answer

A)  You can take the heat and do not stay of of the sun. 
B)  You canʹt take the heat and do not stay out of the sun. 
C)  You can take the heat or stay out of the sun. 
D)  You can take the heat but stay out of the sun. 
A)  You can take the heat and do not stay of of the sun. 
B)  You canʹt take the heat and do not stay out of the sun. 
C)  You can take the heat or stay out of the sun. 
D)  You can take the heat but stay out of the sun.

Question 14

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

Accepted Answer

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

Question 15

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols.
-Jim plays football and Michael plays basketball.

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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 I eat too much, then I?ll exercise.

Accepted Answer

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

Question 18

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.
-It is false that whales are fish and bats are birds.

Accepted Answer

A)  Compound; biconditional; $\leftrightarrow$ 
B)  Compound; disjunction; $\vee$ 
C)  Compound; negation;$\sim$ 
D)  Compound; conjunction; $\wedge$ 
A)  Compound; biconditional; $\leftrightarrow$ 
B)  Compound; disjunction; $\vee$ 
C)  Compound; negation;$\sim$ 
D)  Compound; conjunction; $\wedge$

Question 19

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.
-  
Thirty-one percent of people watch 7 hours of TV each week or 6% do not watch 9 or more hours of TV each week, and 18% watch 8 hours of TV each week.

Accepted Answer

A) True 
 B)False

Question 20

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 + 8 = 20 - 3 or 36 ÷ 3 = 2 + 6

Accepted Answer

A) True 
 B)False

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

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

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 apartment is rented or it is available.

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

Write an equivalent sentence for the statement. -If the box is in the mail, then it should be here by tomorrow. (Hint: Use the fact that p → q is Equivalent to ~p ∨ q.)

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

Write the indicated statement. Use De Morgan's Laws if necessary. -If you like me, then I like you. Converse

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

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

Write an equivalent sentence for the statement. -If you canʹt take the heat, stay out of the sun. (Hint: Use the fact that p → q is equivalent to ~p ∨ q.)

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

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Jim plays football and Michael plays basketball.

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

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 I eat too much, then I?ll exercise.

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. -It is false that whales are fish and bats are birds.

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 + 8 = 20 - 3 or 36 ÷ 3 = 2 + 6

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

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

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these. - p→(q∨p)p \rightarrow(q \vee p)p→(q∨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 apartment is rented or it is available.

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

Write an equivalent sentence for the statement. -If the box is in the mail, then it should be here by tomorrow. (Hint: Use the fact that p → q is Equivalent to ~p ∨ q.)

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent. - (p∨q)∨r,p∨(q∨r)( p \vee q ) \vee r , p \vee ( q \vee r )(p∨q)∨r,p∨(q∨r)

Write the indicated statement. Use De Morgan's Laws if necessary. -If you like me, then I like you. Converse

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

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

Write an equivalent sentence for the statement. -If you canʹt take the heat, stay out of the sun. (Hint: Use the fact that p → q is equivalent to ~p ∨ q.)

Construct a truth table for the statement. - r∨∼(c∧q)r \vee \sim(c \wedge q)r∨∼(c∧q)

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Jim plays football and Michael plays basketball.

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

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 I eat too much, then I?ll exercise.

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. -It is false that whales are fish and bats are birds.

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 + 8 = 20 - 3 or 36 ÷ 3 = 2 + 6

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

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

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

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

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

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

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

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

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