Question 1

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these.
-$$( q \wedge p ) \leftrightarrow \sim ( p \wedge q )$$
A) Tautology
B) Self-contradiction
C) Implication
D) None of these

Accepted Answer

The statement is a self-contradiction because $(q \wedge p)$ and $\sim(p \wedge q)$ cannot both be true at the same time. The left side affirms that both $p$ and $q$ are true, while the right side negates this assertion, making the statement always false.

Question 2

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 eat too much. 
A) $q \rightarrow p$
$$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \mathrm { q } \rightarrow \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$$

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

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

D)$q \rightarrow p$

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

Accepted Answer

The statement "I'll exercise if I eat too much" translates to $p \rightarrow q$, where $p$ is "I eat too much" and $q$ is "I'll exercise". The truth table for $p \rightarrow q$ correctly shows that the statement is true except when $p$ is true and $q$ is false.

Question 3

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

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

Accepted Answer

The statement $p \rightarrow(q \vee p)$ is an implication because it is in the form of "if p, then q or p," which does not necessarily always evaluate to true or false without knowing the truth values of p and q, but it follows the structure of an implication (if-then statement).

Question 4

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these.
-$$\sim p \vee ( \sim p \rightarrow \sim q )$$
A) Implication
B) Self-contradiction
C) Tautology
D) None of these

Accepted Answer

The given statement is a tautology because the disjunction ($\sim p \vee ( \sim p \rightarrow \sim q )$) is always true regardless of the truth values of $p$ and $q$. If $\sim p$ is true, the whole statement is true. If $\sim p$ is false (meaning $p$ is true), then the implication $\sim p \rightarrow \sim q$ is true (since a false premise leads to any conclusion), making the whole statement true again.

Question 5

Construct a truth table for the statement.
-$\sim(p \wedge q) \rightarrow \sim(p \vee q)$
A)
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \wedge \mathrm { q } ) \rightarrow \sim ( \mathrm { p } \vee \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$
B)
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \wedge \mathrm { q } ) \rightarrow \sim ( \mathrm { p } \vee \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$
C)
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \wedge \mathrm { q } ) \rightarrow \sim ( \mathrm { p } \vee \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$
D)
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \wedge \mathrm { q } ) \rightarrow \sim ( \mathrm { p } \vee \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

Accepted Answer

The answer of Construct a truth table for the statement.
-\(\sim(p...

Question 6

Construct a truth table for the statement.
-$\sim(p \rightarrow q) \rightarrow(p \wedge \sim q)$
A)
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \rightarrow \mathrm { q } ) \rightarrow ( \mathrm { p } \wedge \sim \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$
B)
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \rightarrow \mathrm { q } ) \rightarrow ( \mathrm { p } \wedge \sim \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$
C)
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \rightarrow \mathrm { q } ) \rightarrow ( \mathrm { p } \wedge \sim \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$
D)
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim ( \mathrm { p } \rightarrow \mathrm { q } ) \rightarrow ( \mathrm { p } \wedge \sim \mathrm { q } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

Accepted Answer

The answer of Construct a truth table for the statement.
-\(\sim(p...

Question 7

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these.
-$$( p \vee q ) \wedge \sim q$$
A) Tautology
B) Self-contradiction
C) Implication
D) None of these

Accepted Answer

The statement $( p \vee q ) \wedge \sim q$ is not always true (tautology) or always false (self-contradiction). It is also not an implication. It is true when $p$ is true and $q$ is false, so it is "none of these."

Question 8

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, then I eat too much. 
A) $r \rightarrow p$
$\begin{array} { c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { r } \rightarrow \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$

B)$r \rightarrow p$
$\begin{array} { c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { r } \rightarrow \mathrm { p } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

C)$P \rightarrow r$
$\begin{array} { c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { p } \rightarrow \mathrm { r } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

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

Accepted Answer

The correct symbolic representation of "If the food is good, then I eat too much" is $r \rightarrow p$, and the truth table for $r \rightarrow p$ correctly shows that when $r$ is true and $p$ is true, the implication is true; when $r$ is true and $p$ is false, the implication is false; when $r$ is false (regardless of $p$'s value), the implication is true.

Question 9

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. 
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)$(r \vee p) \rightarrow q$
$\begin{array} { l c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { q } & ( \mathrm { r } \vee \mathrm { p } ) \rightarrow \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

Accepted Answer

The answer of Write the compound statement in symbols. Then...

Question 10

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication), or none of these.
-$$p \leftrightarrow q$$
A) Tautology
B) Self-contradiction
C) Implication
D) None of these

Accepted Answer

The statement $p \leftrightarrow q$ is a biconditional statement, meaning it is true when both $p$ and $q$ have the same truth value (both true or both false) and false otherwise. It is not a tautology, self-contradiction, or an implication by itself without additional context.

Question 11

Write the compound statement in symbols. Then construct a truth table for the symbolic statement.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-If the food is not good, I won?t eat too much. 
A)$\sim(r \rightarrow p)$
$\begin{array} { c c c } 
\mathrm { r } & \mathrm { p } & \sim ( \mathrm { r } \rightarrow \mathrm { p } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

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

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

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

Accepted Answer

The correct symbolic representation of "If the food is not good, I won't eat too much" is $\sim r \rightarrow \sim p$, which matches option D. The truth table for $\sim r \rightarrow \sim p$ correctly reflects the logic of conditional statements, where the statement is false only when the antecedent is true and the consequent is false.

Question 12

Write the compound statement in symbols. Then construct a truth table for the symbolic statement.
Let r = ʺThe food is good,ʺ p = ʺI eat too much,ʺ q = ʺIʹll exercise.ʺ
-The food is good and if I eat too much, then I?ll exercise. 
A) $(r \wedge p) \rightarrow q$
$\begin{array} { c c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { q } & \left( \mathrm { r } { \wedge } \mathrm { p } \right) \rightarrow \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

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

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

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

Accepted Answer

The correct symbolic representation of the statement "The food is good and if I eat too much, then I'll exercise" is $r \wedge(p \rightarrow q)$, which combines the condition of the food being good (r) with the conditional statement that if eating too much (p) then exercising (q). The truth table for D accurately reflects the logical outcomes of this compound statement.

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
-If the food is good or if I eat too much, I?ll exercise. 
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)$(r \vee p) \rightarrow q$
$\begin{array} { l l l c } 
\mathrm { r } & \mathrm { p } & \mathrm { q } & ( \mathrm { r } \vee \mathrm { p } ) \rightarrow \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

Accepted Answer

The correct symbolic representation of the statement "If the food is good or if I eat too much, I'll exercise" is $(r \vee p) \rightarrow q$, which means if either $r$ (the food is good) or $p$ (I eat too much) is true, then $q$ (I'll exercise) will follow.

Question 14

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

Accepted Answer

The given statement is an implication because it has the form of $A \rightarrow B$, where $A$ is the negation of $[( p \rightarrow q ) \wedge ( q \rightarrow p )]$ and $B$ is $\sim ( p \leftrightarrow q )$. The statement essentially says that if it is not the case that $p$ implies $q$ and $q$ implies $p$ simultaneously, then $p$ and $q$ do not have the same truth value. This is a conditional statement, making it an implication.

Question 15

Construct a truth table for the statement.
-$( \sim \mathrm { p } \vee \sim \mathrm { q } ) \rightarrow \sim ( \mathrm { q } \wedge \mathrm { p } )$
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) 
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \left( \sim \mathrm { p } _ { \vee } \sim \mathrm { q } \right) \rightarrow \sim ( \mathrm { q } \wedge \mathrm { p } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

Accepted Answer

The statement $( \sim \mathrm { p } \vee \sim \mathrm { q } ) \rightarrow \sim ( \mathrm { q } \wedge \mathrm { p } )$ is a tautology, meaning it is always true regardless of the truth values of $p$ and $q$, except when both $p$ and $q$ are false, which makes the antecedent false and the consequent true, still validating the conditional statement.

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 I eat too much, then I?ll exercise. 
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) $q \rightarrow p$ 
$\begin{array}{ccc}
\mathrm{p} & \mathrm{q} & \mathrm{q} \rightarrow \mathrm{p} \
\hline \mathrm{T} & \mathrm{T} & \mathrm{T} \
\mathrm{T} & \mathrm{F} & \mathrm{T} \
\mathrm{F} & \mathrm{T} & \mathrm{F} \
\mathrm{F} & \mathrm{F} & \mathrm{T}
\end{array}$

Accepted Answer

The statement "If I eat too much, then Iʹll exercise" directly translates to $p \rightarrow q$, and the truth table for $p \rightarrow q$ correctly shows that when $p$ is true and $q$ is false, the implication is false, and in all other cases, the implication is true.

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
-I?ll exercise if I don?t eat too much. 
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)$\sim \mathrm{p} \rightarrow \mathrm{q}$
$\begin{array} { c c c } 
\mathrm { p } & \mathrm { q } & \sim \mathrm { p } \rightarrow \mathrm { q } \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F }
\end{array}$

Accepted Answer

The statement "I'll exercise if I don't eat too much" translates to "If not p, then q" or symbolically, $\sim p \rightarrow q$. The truth table for $\sim p \rightarrow q$ correctly reflects the logic of conditional statements, where the statement is false only when the antecedent is true ($\sim p$ is true) and the consequent (q) is false.

Question 18

Construct a truth table for the statement.
-$(\sim \mathrm{p} \rightarrow \mathrm{q}) \rightarrow(\mathrm{q} \rightarrow \sim \mathrm{r})$
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)
$\begin{array} { c c c c } 
\mathrm { p } & \mathrm { q } & \mathrm { r } & ( \sim \mathrm { p } \rightarrow \mathrm { q } ) \leftrightarrow ( \mathrm { q } \rightarrow \sim \mathrm { r } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

Accepted Answer

The truth table for $(\sim \mathrm{p} \rightarrow \mathrm{q}) \rightarrow(\mathrm{q} \rightarrow \sim \mathrm{r})$ matches the one provided in option C.

Question 19

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

Accepted Answer

The correct symbolic representation of "If I exercise, then I won't eat too much" is $q \rightarrow \sim p$, and the truth table for $q \rightarrow \sim p$ correctly reflects the logical relationship, where the statement is true except when $q$ is true and $p$ is also true (which contradicts the given statement).

Question 20

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 the food won?t be good and I won?t eat too much. 
A)$q \rightarrow(\sim r \wedge \sim p)$
$\begin{array} { l c c c } 
\mathrm { r } & \mathrm { p } & \mathrm { q } & \mathrm { q } \rightarrow ( \sim \mathrm { r } \wedge \sim \mathrm { p } ) \
\hline \mathrm { T } & \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { T } & \mathrm { F } & \mathrm { T } & \mathrm { F } \
\mathrm { T } & \mathrm { F } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { T } & \mathrm { T } & \mathrm { F } \
\mathrm { F } & \mathrm { T } & \mathrm { F } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { T } & \mathrm { T } \
\mathrm { F } & \mathrm { F } & \mathrm { F } & \mathrm { T }
\end{array}$

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

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

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

Accepted Answer

The statement "If I exercise, then the food won’t be good and I won’t eat too much" translates to $q \rightarrow (\sim r \wedge \sim p)$. The truth table in option A correctly reflects this logical structure.

Quiz 3: Logic

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

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 eat too much.

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

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

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

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

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

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, then I 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.

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

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

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

Write the compound statement in symbols. 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.

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

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

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.

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.

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

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

Quiz 3: Logic

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

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 eat too much.

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)

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

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

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

Determine whether the statement is a self-contradiction, an implication, a tautology (that is not also an implication) , or none of these. - (p∨q) ∧∼q( p \vee q ) \wedge \sim q(p∨q) ∧∼q