Question 1

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

Accepted Answer

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

Question 2

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols.
-Jim does not play football and Michael does not play basketball.

Accepted Answer

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

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 + 8 = 20 - 3 and 36 ÷ 3 = 6 + 2

Accepted Answer

A) True 
 B)False

Question 4

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

Accepted Answer

A) True 
 B)False

Question 5

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.
-0 > -3 or 3 ≥ 10

Accepted Answer

A) True 
 B)False

Question 6

Write the indicated statement. Use De Morgan's Laws if necessary.
-If the chores are done, then we will go to the carnival and we will eat cotton candy.
Contrapositive

Accepted Answer

A)  If we do not go to the carnival and we do not eat cotton candy, then the chores are not done. 
B)  If the chores are not done, then we will not go to the carnival or we will not eat cotton candy. 
C)  If we do not go to the carnival or we do not eat cotton candy, then the chores are not done. 
D)  If we go to the carnival and we eat cotton candy, then the chores are done. 
A)  If we do not go to the carnival and we do not eat cotton candy, then the chores are not done. 
B)  If the chores are not done, then we will not go to the carnival or we will not eat cotton candy. 
C)  If we do not go to the carnival or we do not eat cotton candy, then the chores are not done. 
D)  If we go to the carnival and we eat cotton candy, then the chores are done.

Question 7

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols.
-Jim does not play football or Michael does not play basketball.

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

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 tomorrow is not Saturday then today is Friday if and only if tomorrow is Saturday.

Accepted Answer

A)  $( \sim \mathrm { p } \rightarrow \mathrm { q } ) \rightarrow \mathrm { p }$; conditional 
B)  $\sim \mathrm { p } \rightarrow ( \mathrm { q } \leftrightarrow \mathrm { p } )$; conditional 
C)  $\sim [ ( p \rightarrow q ) \leftrightarrow  p ]$; negation 
D)  $( \sim \mathrm { p } \rightarrow \mathrm { q } ) \leftrightarrow  \mathrm { p }$; 
biconditional 
A)  $( \sim \mathrm { p } \rightarrow \mathrm { q } ) \rightarrow \mathrm { p }$; conditional 
B)  $\sim \mathrm { p } \rightarrow ( \mathrm { q } \leftrightarrow \mathrm { p } )$; conditional 
C)  $\sim [ ( p \rightarrow q ) \leftrightarrow  p ]$; negation 
D)  $( \sim \mathrm { p } \rightarrow \mathrm { q } ) \leftrightarrow  \mathrm { p }$; 
biconditional

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

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.
-  
If older viewers watch fewer drama programs than younger viewers and younger viewers watch dramas less than 25% of the time, then older viewers watch drama programs less than 25% of the time.

Accepted Answer

A) True 
 B)False

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Determine which, if any, of the three statements are equivalent.
-I. Jan is well or Jan is still recovering.
II. If Jan is still recovering, then Jan is not well.
III. If Jan is well, then Jan is not still recovering.

Accepted Answer

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

Question 18

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

Accepted Answer

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

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.
-0 > -7 or 4 ≥ 10, and -4 ≤ 7

Accepted Answer

A) True 
 B)False

Question 20

Identify the standard form of the argument.
-$ p \rightarrow q $
$ \frac {\sim q }
 {\therefore \sim p} $

Accepted Answer

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

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

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Jim does not play football and Michael does not play basketball.

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 and 36 ÷ 3 = 6 + 2

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

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. -0 > -3 or 3 ≥ 10

Write the indicated statement. Use De Morgan's Laws if necessary. -If the chores are done, then we will go to the carnival and we will eat cotton candy. Contrapositive

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Jim does not play football or Michael does not play basketball.

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

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

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

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

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

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

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

Determine which, if any, of the three statements are equivalent. -I. Jan is well or Jan is still recovering. II. If Jan is still recovering, then Jan is not well. III. If Jan is well, then Jan is not still recovering.

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

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. -0 > -7 or 4 ≥ 10, and -4 ≤ 7

Identify the standard form of the argument. - $p \rightarrow q$ $\frac {\sim q } {\therefore \sim p}$

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

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

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Jim does not play football and Michael does not play basketball.

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 and 36 ÷ 3 = 6 + 2

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

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. -0 > -3 or 3 ≥ 10

Write the indicated statement. Use De Morgan's Laws if necessary. -If the chores are done, then we will go to the carnival and we will eat cotton candy. Contrapositive

Let p represent the statement, ʺJim plays footballʺ, and let q represent ʺMichael plays basketballʺ. Convert the compound statements into symbols. -Jim does not play football or Michael does not play basketball.

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

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

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

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

Given p is true, q is true, and r is false, find the truth value of the statement. - (q∨r)↔(p∧q)( q \vee r ) \leftrightarrow ( p \wedge q )(q∨r)↔(p∧q)

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

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

Determine which, if any, of the three statements are equivalent. -I. Jan is well or Jan is still recovering. II. If Jan is still recovering, then Jan is not well. III. If Jan is well, then Jan is not still recovering.

Construct a truth table for the statement. - ∼(p∧s)→(p→(∼t∧s))\sim(p \wedge s) \rightarrow(p \rightarrow(\sim t \wedge s))∼(p∧s)→(p→(∼t∧s))

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. -0 > -7 or 4 ≥ 10, and -4 ≤ 7

Identify the standard form of the argument. - p→q p \rightarrow q p→q ∼q∴∼p \frac {\sim q } {\therefore \sim p} ∴∼p∼q​

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

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

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

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

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

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

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

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

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

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

Identify the standard form of the argument. - $p \rightarrow q$ $\frac {\sim q } {\therefore \sim p}$