Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Translate the statement into symbols then construct a truth table.
-$ \mathrm{p}= $ The forest is dark.
$ \mathrm{q}= $ The moon is full.
The forest is dark or the moon is full.

Accepted Answer

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

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

Answer the question.
-A restaurant has the following statement on the menu: ʺAll dinners are served with a choice of: Soup or Salad, and Potatoes or Pasta, and Corn or Beans.ʺ A customer asks for salad, potatoes, And pasta. Is this order permissible?

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

A)  If the puppy is trained, then the puppy behaves will and his owners are happy. 
B)  The puppy is trained and the puppy behaves well if his owners are happy. 
C)  If the puppy is trained or the puppy behaves well, then his owners are happy. 
D)  If the puppy is trained and the puppy behaves well, then his owners are happy. 
A)  If the puppy is trained, then the puppy behaves will and his owners are happy. 
B)  The puppy is trained and the puppy behaves well if his owners are happy. 
C)  If the puppy is trained or the puppy behaves well, then his owners are happy. 
D)  If the puppy is trained and the puppy behaves well, then his owners are happy.

Question 8

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent.
-~(p ∧ q), ~p ∧ ~q

Accepted Answer

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

Question 9

Write an equivalent sentence for the statement.
-If you are mistaken then you are wrong, and if you are wrong then you are mistaken. (Hint: Use The fact that (p → q) ∧ (q → p) is equivalent to p ↔ q.)

Accepted Answer

A)  You are mistaken or you are wrong. 
B)  You are mistaken and wrong. 
C)  You are mistaken if and only if you are wrong. 
D)  You are mistaken if you are wrong. 
A)  You are mistaken or you are wrong. 
B)  You are mistaken and wrong. 
C)  You are mistaken if and only if you are wrong. 
D)  You are mistaken if you are wrong.

Question 10

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

Accepted Answer

A) 
$\begin{array} { c c c } 
\mathrm { s } & \mathrm { q } & \sim \mathrm { s } _\rightarrow ( \sim \mathrm { s } \wedge \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
B) 
$\begin{array} { c c c } 
\mathrm { s } & \mathrm { q } & \sim \mathrm { s } _\rightarrow ( \sim \mathrm { s } \wedge \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
C) 
$\begin{array} { c c c } 
\mathrm { s } & \mathrm { q } & \sim \mathrm { s } _\rightarrow ( \sim \mathrm { s } \wedge \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
D) 
$\begin{array} { c c c } 
\mathrm { s } & \mathrm { q } & \sim \mathrm { s } 
_\rightarrow ( \sim \mathrm { s } \wedge \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$ 
A) 
$\begin{array} { c c c } 
\mathrm { s } & \mathrm { q } & \sim \mathrm { s } _\rightarrow ( \sim \mathrm { s } \wedge \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
B) 
$\begin{array} { c c c } 
\mathrm { s } & \mathrm { q } & \sim \mathrm { s } _\rightarrow ( \sim \mathrm { s } \wedge \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
C) 
$\begin{array} { c c c } 
\mathrm { s } & \mathrm { q } & \sim \mathrm { s } _\rightarrow ( \sim \mathrm { s } \wedge \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$ 
D) 
$\begin{array} { c c c } 
\mathrm { s } & \mathrm { q } & \sim \mathrm { s } 
_\rightarrow ( \sim \mathrm { s } \wedge \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

Question 11

Write a negation of the statement.
-Some citizens obey traffic laws.

Accepted Answer

A)  All citizens obey traffic laws. 
B)  No citizens do not obey traffic laws. 
C)  Some citizens do not obey traffic laws. 
D)  No citizens obey traffic laws. 
A)  All citizens obey traffic laws. 
B)  No citizens do not obey traffic laws. 
C)  Some citizens do not obey traffic laws. 
D)  No citizens obey traffic laws.

Question 12

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.
-If you forget to bring the book back to the library, you will have to pay a fine.

Accepted Answer

A)  Simple statement 
B)  Compound; biconditional; $\leftrightarrow$ 
C)  Compound; conditional; → 
D)  Compound; conjunction; $\wedge$ 
A)  Simple statement 
B)  Compound; biconditional; $\leftrightarrow$ 
C)  Compound; conditional; → 
D)  Compound; conjunction; $\wedge$

Question 13

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
-I?ll exercise if I don?t eat too much.

Accepted Answer

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

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

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

Question 14

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 exercise, then I won?t eat too much.

Accepted Answer

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

Question 15

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 good and if I eat too much, then I?ll exercise.

Accepted Answer

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

Question 16

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 good or if I eat too much, I?ll exercise.

Accepted Answer

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

Question 17

Write the contrapositive of the statement. Then use the contrapositive to determine whether to conditional statement is true or false.
-If the triangle is not equilateral, then the three sides of the triangle are not equal.

Accepted Answer

A)  If three sides of a triangle are not equal, then the triangle is not equilateral. true 
B)  If three sides of a triangle are equal, then the triangle is equilateral. false 
C)  If three sides of a triangle are not equal, then the triangle is not equilateral. false 
D)  If three sides of a triangle are equal, then the triangle is equilateral. true 
A)  If three sides of a triangle are not equal, then the triangle is not equilateral. true 
B)  If three sides of a triangle are equal, then the triangle is equilateral. false 
C)  If three sides of a triangle are not equal, then the triangle is not equilateral. false 
D)  If three sides of a triangle are equal, then the triangle is equilateral. true

Question 18

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

Accepted Answer

A) True 
 B)False

Question 19

Write a negation of the statement.
-All squares are parallelograms.

Accepted Answer

A)  Some squares are parallelograms. 
B)  Some squares are not parallelograms. 
C)  All squares are not parallelograms. 
D)  No squares are parallelograms. 
A)  Some squares are parallelograms. 
B)  Some squares are not parallelograms. 
C)  All squares are not parallelograms. 
D)  No squares are parallelograms.

Question 20

Determine which, if any, of the three statements are equivalent.
-I. If it is sunny and the pool is open, then I will go swimming.
II. If I do not go swimming, then it it is not the case that it is sunny or the pool is open.
III. It is sunny and the pool is open, or I will go swimming.

Accepted Answer

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

Identify the standard form of the argument. - p\rightarrowq

Convert the compound statement into words. - p= "The food tastes delicious." q= "We eat a lot." r= "Nobody has dessert." (q\veep)\wedger

Translate the statement into symbols then construct a truth table. - $\mathrm{p}=$ The forest is dark. $\mathrm{q}=$ The moon is full. The forest is dark or the moon is full.

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

Answer the question. -A restaurant has the following statement on the menu: ʺAll dinners are served with a choice of: Soup or Salad, and Potatoes or Pasta, and Corn or Beans.ʺ A customer asks for salad, potatoes, And pasta. Is this order permissible?

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

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

Use DeMorganʹs laws or a truth table to determine whether the two statements are equivalent. -~(p ∧ q), ~p ∧ ~q

Write an equivalent sentence for the statement. -If you are mistaken then you are wrong, and if you are wrong then you are mistaken. (Hint: Use The fact that (p → q) ∧ (q → p) is equivalent to p ↔ q.)

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

Write a negation of the statement. -Some citizens obey traffic laws.

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 -I?ll exercise if I don?t eat too much.

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 exercise, then I won?t eat too much.

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 good and if I eat too much, then I?ll exercise.

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 good or if I eat too much, I?ll exercise.

Write the contrapositive of the statement. Then use the contrapositive to determine whether to conditional statement is true or false. -If the triangle is not equilateral, then the three sides of the triangle are not equal.

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

Write a negation of the statement. -All squares are parallelograms.

Determine which, if any, of the three statements are equivalent. -I. If it is sunny and the pool is open, then I will go swimming. II. If I do not go swimming, then it it is not the case that it is sunny or the pool is open. III. It is sunny and the pool is open, or I will go swimming.

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