Question 1

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression.
-(∼P ⊃ P) $ \lor $ (A ⊃ P)

Accepted Answer

The answer of Assume A, B, C are true; X,...

Question 2

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression.
-(∼P ⊃ P) $ \lor $ (P ⊃ A)

Accepted Answer

The answer of Assume A, B, C are true; X,...

Question 3

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression.
-∼(Q ⊃ C) $ \lor $ (Z • ∼X)

Accepted Answer

The answer of Assume A, B, C are true; X,...

Question 4

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression.
-∼[(Z ⊃ B) • (P ⊃ C)] $ \lor $ [(X • Y) ≡ A]

Accepted Answer

The answer of Assume A, B, C are true; X,...

Question 5

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression.
-(P ⊃ ∼Q) $ \lor $ ∼P

Accepted Answer

The answer of Assume A, B, C are true; X,...

Question 6

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression.
-(P ≡ Q) $ \lor $ (P ≡ ∼Q)

Accepted Answer

The answer of Assume A, B, C are true; X,...

Question 7

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression.
-[(P $ \lor $ Q) ⊃ X] ≡ ∼(P $ \lor $ Q)

Accepted Answer

The answer of Assume A, B, C are true; X,...

Question 8

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression.
-[(P • Q) $ \lor $ (∼P • Q)] $ \lor $ [(P • ∼Q) $ \lor $ (∼P • ∼Q)]

Accepted Answer

The answer of Assume A, B, C are true; X,...

Question 9

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression.
-∼[(A ⊃ P) $ \lor $ (A ⊃ Q)] • (P • Q)

Accepted Answer

The answer of Assume A, B, C are true; X,...

Question 10

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment.
For exercises with only one propositional variable, the standard assignment is:
 $\begin{array} {| l | }
\hline  \alpha\\hline \text {1 }\\hline \text {0 }\\hline
\end{array}$
 
For exercises with two propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | } 
\hline \mathbf { n } & \boldsymbol { \beta } \
\hline 1 & 1 \
\hline 1 & 0 \
\hline 0 & 1 \
\hline 0 & 0 \
\hline
\end{array}$$ 
For exercises with three propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | c | } 
\hline \alpha & \beta & \gamma \
\hline 1 & 1 & 1 \
\hline 1 & 1 & 0 \
\hline 1 & 0 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 1 & 0 \
\hline 0& 0 & 1 \
\hline 0 & 0 &0\
\hline
\end{array}$$ 
For exercises with four propositional variables, the standard assignment is:
 $\begin{array}{|c|c|c|c|}
\hline\alpha & \beta & \gamma & \delta \
\hline 1 & 1 & 1 & 1 \
\hline 1 & 1 & 1 & 0 \
\hline 1 & 1 & 0 & 1 \
\hline 1 & 1 & 0 & 0\
\hline 1 & 0 & 1 & 1 \
\hline 1 & 0 & 1 & 0 \
\hline 1 & 0 & 0 & 1 \
\hline 1 & 0 & 0 & 0 \
\hline 0 & 1 & 1 & 1 \
\hline 0 & 1 & 1 & 0 \
\hline 0 & 1 & 0 & 1\
\hline 0 & 1 & 0 & 0 \
\hline 0 & 0 & 1 & 1 \
\hline 0 & 0 & 1 & 0 \
\hline 0 & 0 & 0 & 1 \
\hline 0 & 0 & 0 & 0\\hline
\end{array}$ 
Complete truth tables for each of the following propositions.
-(B ⊃ B) $ \lor $ ∼B
(B ⊃ B) $ \lor $ ∼B

Accepted Answer

The answer of Note: the solutions to most of the...

Question 11

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment.
For exercises with only one propositional variable, the standard assignment is:
 $\begin{array} {| l | }
\hline  \alpha\\hline \text {1 }\\hline \text {0 }\\hline
\end{array}$
 
For exercises with two propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | } 
\hline \mathbf { n } & \boldsymbol { \beta } \
\hline 1 & 1 \
\hline 1 & 0 \
\hline 0 & 1 \
\hline 0 & 0 \
\hline
\end{array}$$ 
For exercises with three propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | c | } 
\hline \alpha & \beta & \gamma \
\hline 1 & 1 & 1 \
\hline 1 & 1 & 0 \
\hline 1 & 0 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 1 & 0 \
\hline 0& 0 & 1 \
\hline 0 & 0 &0\
\hline
\end{array}$$ 
For exercises with four propositional variables, the standard assignment is:
 $\begin{array}{|c|c|c|c|}
\hline\alpha & \beta & \gamma & \delta \
\hline 1 & 1 & 1 & 1 \
\hline 1 & 1 & 1 & 0 \
\hline 1 & 1 & 0 & 1 \
\hline 1 & 1 & 0 & 0\
\hline 1 & 0 & 1 & 1 \
\hline 1 & 0 & 1 & 0 \
\hline 1 & 0 & 0 & 1 \
\hline 1 & 0 & 0 & 0 \
\hline 0 & 1 & 1 & 1 \
\hline 0 & 1 & 1 & 0 \
\hline 0 & 1 & 0 & 1\
\hline 0 & 1 & 0 & 0 \
\hline 0 & 0 & 1 & 1 \
\hline 0 & 0 & 1 & 0 \
\hline 0 & 0 & 0 & 1 \
\hline 0 & 0 & 0 & 0\\hline
\end{array}$ 
Complete truth tables for each of the following propositions.
-(D ≡ ∼D) ≡ (∼D ≡ D)

Accepted Answer

The answer of Note: the solutions to most of the...

Question 12

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment.
For exercises with only one propositional variable, the standard assignment is:
 $\begin{array} {| l | }
\hline  \alpha\\hline \text {1 }\\hline \text {0 }\\hline
\end{array}$
 
For exercises with two propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | } 
\hline \mathbf { n } & \boldsymbol { \beta } \
\hline 1 & 1 \
\hline 1 & 0 \
\hline 0 & 1 \
\hline 0 & 0 \
\hline
\end{array}$$ 
For exercises with three propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | c | } 
\hline \alpha & \beta & \gamma \
\hline 1 & 1 & 1 \
\hline 1 & 1 & 0 \
\hline 1 & 0 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 1 & 0 \
\hline 0& 0 & 1 \
\hline 0 & 0 &0\
\hline
\end{array}$$ 
For exercises with four propositional variables, the standard assignment is:
 $\begin{array}{|c|c|c|c|}
\hline\alpha & \beta & \gamma & \delta \
\hline 1 & 1 & 1 & 1 \
\hline 1 & 1 & 1 & 0 \
\hline 1 & 1 & 0 & 1 \
\hline 1 & 1 & 0 & 0\
\hline 1 & 0 & 1 & 1 \
\hline 1 & 0 & 1 & 0 \
\hline 1 & 0 & 0 & 1 \
\hline 1 & 0 & 0 & 0 \
\hline 0 & 1 & 1 & 1 \
\hline 0 & 1 & 1 & 0 \
\hline 0 & 1 & 0 & 1\
\hline 0 & 1 & 0 & 0 \
\hline 0 & 0 & 1 & 1 \
\hline 0 & 0 & 1 & 0 \
\hline 0 & 0 & 0 & 1 \
\hline 0 & 0 & 0 & 0\\hline
\end{array}$ 
Complete truth tables for each of the following propositions.
-∼[F • (F ⊃ F)]
∼[F • (F ⊃ F)]

Accepted Answer

The answer of Note: the solutions to most of the...

Question 13

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment.
For exercises with only one propositional variable, the standard assignment is:
 $\begin{array} {| l | }
\hline  \alpha\\hline \text {1 }\\hline \text {0 }\\hline
\end{array}$
 
For exercises with two propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | } 
\hline \mathbf { n } & \boldsymbol { \beta } \
\hline 1 & 1 \
\hline 1 & 0 \
\hline 0 & 1 \
\hline 0 & 0 \
\hline
\end{array}$$ 
For exercises with three propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | c | } 
\hline \alpha & \beta & \gamma \
\hline 1 & 1 & 1 \
\hline 1 & 1 & 0 \
\hline 1 & 0 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 1 & 0 \
\hline 0& 0 & 1 \
\hline 0 & 0 &0\
\hline
\end{array}$$ 
For exercises with four propositional variables, the standard assignment is:
 $\begin{array}{|c|c|c|c|}
\hline\alpha & \beta & \gamma & \delta \
\hline 1 & 1 & 1 & 1 \
\hline 1 & 1 & 1 & 0 \
\hline 1 & 1 & 0 & 1 \
\hline 1 & 1 & 0 & 0\
\hline 1 & 0 & 1 & 1 \
\hline 1 & 0 & 1 & 0 \
\hline 1 & 0 & 0 & 1 \
\hline 1 & 0 & 0 & 0 \
\hline 0 & 1 & 1 & 1 \
\hline 0 & 1 & 1 & 0 \
\hline 0 & 1 & 0 & 1\
\hline 0 & 1 & 0 & 0 \
\hline 0 & 0 & 1 & 1 \
\hline 0 & 0 & 1 & 0 \
\hline 0 & 0 & 0 & 1 \
\hline 0 & 0 & 0 & 0\\hline
\end{array}$ 
Complete truth tables for each of the following propositions.
-U ≡ (Z ⊃ U)

Accepted Answer

The answer of Note: the solutions to most of the...

Question 14

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment.
For exercises with only one propositional variable, the standard assignment is:
 $\begin{array} {| l | }
\hline  \alpha\\hline \text {1 }\\hline \text {0 }\\hline
\end{array}$
 
For exercises with two propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | } 
\hline \mathbf { n } & \boldsymbol { \beta } \
\hline 1 & 1 \
\hline 1 & 0 \
\hline 0 & 1 \
\hline 0 & 0 \
\hline
\end{array}$$ 
For exercises with three propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | c | } 
\hline \alpha & \beta & \gamma \
\hline 1 & 1 & 1 \
\hline 1 & 1 & 0 \
\hline 1 & 0 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 1 & 0 \
\hline 0& 0 & 1 \
\hline 0 & 0 &0\
\hline
\end{array}$$ 
For exercises with four propositional variables, the standard assignment is:
 $\begin{array}{|c|c|c|c|}
\hline\alpha & \beta & \gamma & \delta \
\hline 1 & 1 & 1 & 1 \
\hline 1 & 1 & 1 & 0 \
\hline 1 & 1 & 0 & 1 \
\hline 1 & 1 & 0 & 0\
\hline 1 & 0 & 1 & 1 \
\hline 1 & 0 & 1 & 0 \
\hline 1 & 0 & 0 & 1 \
\hline 1 & 0 & 0 & 0 \
\hline 0 & 1 & 1 & 1 \
\hline 0 & 1 & 1 & 0 \
\hline 0 & 1 & 0 & 1\
\hline 0 & 1 & 0 & 0 \
\hline 0 & 0 & 1 & 1 \
\hline 0 & 0 & 1 & 0 \
\hline 0 & 0 & 0 & 1 \
\hline 0 & 0 & 0 & 0\\hline
\end{array}$ 
Complete truth tables for each of the following propositions.
-(I ⊃ J) $ \lor $ (J ⊃ I)

Accepted Answer

The answer of Note: the solutions to most of the...

Question 15

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment.
For exercises with only one propositional variable, the standard assignment is:
 $\begin{array} {| l | }
\hline  \alpha\\hline \text {1 }\\hline \text {0 }\\hline
\end{array}$
 
For exercises with two propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | } 
\hline \mathbf { n } & \boldsymbol { \beta } \
\hline 1 & 1 \
\hline 1 & 0 \
\hline 0 & 1 \
\hline 0 & 0 \
\hline
\end{array}$$ 
For exercises with three propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | c | } 
\hline \alpha & \beta & \gamma \
\hline 1 & 1 & 1 \
\hline 1 & 1 & 0 \
\hline 1 & 0 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 1 & 0 \
\hline 0& 0 & 1 \
\hline 0 & 0 &0\
\hline
\end{array}$$ 
For exercises with four propositional variables, the standard assignment is:
 $\begin{array}{|c|c|c|c|}
\hline\alpha & \beta & \gamma & \delta \
\hline 1 & 1 & 1 & 1 \
\hline 1 & 1 & 1 & 0 \
\hline 1 & 1 & 0 & 1 \
\hline 1 & 1 & 0 & 0\
\hline 1 & 0 & 1 & 1 \
\hline 1 & 0 & 1 & 0 \
\hline 1 & 0 & 0 & 1 \
\hline 1 & 0 & 0 & 0 \
\hline 0 & 1 & 1 & 1 \
\hline 0 & 1 & 1 & 0 \
\hline 0 & 1 & 0 & 1\
\hline 0 & 1 & 0 & 0 \
\hline 0 & 0 & 1 & 1 \
\hline 0 & 0 & 1 & 0 \
\hline 0 & 0 & 0 & 1 \
\hline 0 & 0 & 0 & 0\\hline
\end{array}$ 
Complete truth tables for each of the following propositions.
-(K ? L) ? (?K ?L)

Accepted Answer

The answer of Note: the solutions to most of the...

Question 16

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment.
For exercises with only one propositional variable, the standard assignment is:
 $\begin{array} {| l | }
\hline  \alpha\\hline \text {1 }\\hline \text {0 }\\hline
\end{array}$
 
For exercises with two propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | } 
\hline \mathbf { n } & \boldsymbol { \beta } \
\hline 1 & 1 \
\hline 1 & 0 \
\hline 0 & 1 \
\hline 0 & 0 \
\hline
\end{array}$$ 
For exercises with three propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | c | } 
\hline \alpha & \beta & \gamma \
\hline 1 & 1 & 1 \
\hline 1 & 1 & 0 \
\hline 1 & 0 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 1 & 0 \
\hline 0& 0 & 1 \
\hline 0 & 0 &0\
\hline
\end{array}$$ 
For exercises with four propositional variables, the standard assignment is:
 $\begin{array}{|c|c|c|c|}
\hline\alpha & \beta & \gamma & \delta \
\hline 1 & 1 & 1 & 1 \
\hline 1 & 1 & 1 & 0 \
\hline 1 & 1 & 0 & 1 \
\hline 1 & 1 & 0 & 0\
\hline 1 & 0 & 1 & 1 \
\hline 1 & 0 & 1 & 0 \
\hline 1 & 0 & 0 & 1 \
\hline 1 & 0 & 0 & 0 \
\hline 0 & 1 & 1 & 1 \
\hline 0 & 1 & 1 & 0 \
\hline 0 & 1 & 0 & 1\
\hline 0 & 1 & 0 & 0 \
\hline 0 & 0 & 1 & 1 \
\hline 0 & 0 & 1 & 0 \
\hline 0 & 0 & 0 & 1 \
\hline 0 & 0 & 0 & 0\\hline
\end{array}$ 
Complete truth tables for each of the following propositions.
-(M $ \lor $ N) • (M $ \lor $ ?N)

Accepted Answer

The answer of Note: the solutions to most of the...

Question 17

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment.
For exercises with only one propositional variable, the standard assignment is:
 $\begin{array} {| l | }
\hline  \alpha\\hline \text {1 }\\hline \text {0 }\\hline
\end{array}$
 
For exercises with two propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | } 
\hline \mathbf { n } & \boldsymbol { \beta } \
\hline 1 & 1 \
\hline 1 & 0 \
\hline 0 & 1 \
\hline 0 & 0 \
\hline
\end{array}$$ 
For exercises with three propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | c | } 
\hline \alpha & \beta & \gamma \
\hline 1 & 1 & 1 \
\hline 1 & 1 & 0 \
\hline 1 & 0 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 1 & 0 \
\hline 0& 0 & 1 \
\hline 0 & 0 &0\
\hline
\end{array}$$ 
For exercises with four propositional variables, the standard assignment is:
 $\begin{array}{|c|c|c|c|}
\hline\alpha & \beta & \gamma & \delta \
\hline 1 & 1 & 1 & 1 \
\hline 1 & 1 & 1 & 0 \
\hline 1 & 1 & 0 & 1 \
\hline 1 & 1 & 0 & 0\
\hline 1 & 0 & 1 & 1 \
\hline 1 & 0 & 1 & 0 \
\hline 1 & 0 & 0 & 1 \
\hline 1 & 0 & 0 & 0 \
\hline 0 & 1 & 1 & 1 \
\hline 0 & 1 & 1 & 0 \
\hline 0 & 1 & 0 & 1\
\hline 0 & 1 & 0 & 0 \
\hline 0 & 0 & 1 & 1 \
\hline 0 & 0 & 1 & 0 \
\hline 0 & 0 & 0 & 1 \
\hline 0 & 0 & 0 & 0\\hline
\end{array}$ 
Complete truth tables for each of the following propositions.
-(V ? W) • (V ? ?W)

Accepted Answer

The answer of Note: the solutions to most of the...

Question 18

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment.
For exercises with only one propositional variable, the standard assignment is:
 $\begin{array} {| l | }
\hline  \alpha\\hline \text {1 }\\hline \text {0 }\\hline
\end{array}$
 
For exercises with two propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | } 
\hline \mathbf { n } & \boldsymbol { \beta } \
\hline 1 & 1 \
\hline 1 & 0 \
\hline 0 & 1 \
\hline 0 & 0 \
\hline
\end{array}$$ 
For exercises with three propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | c | } 
\hline \alpha & \beta & \gamma \
\hline 1 & 1 & 1 \
\hline 1 & 1 & 0 \
\hline 1 & 0 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 1 & 0 \
\hline 0& 0 & 1 \
\hline 0 & 0 &0\
\hline
\end{array}$$ 
For exercises with four propositional variables, the standard assignment is:
 $\begin{array}{|c|c|c|c|}
\hline\alpha & \beta & \gamma & \delta \
\hline 1 & 1 & 1 & 1 \
\hline 1 & 1 & 1 & 0 \
\hline 1 & 1 & 0 & 1 \
\hline 1 & 1 & 0 & 0\
\hline 1 & 0 & 1 & 1 \
\hline 1 & 0 & 1 & 0 \
\hline 1 & 0 & 0 & 1 \
\hline 1 & 0 & 0 & 0 \
\hline 0 & 1 & 1 & 1 \
\hline 0 & 1 & 1 & 0 \
\hline 0 & 1 & 0 & 1\
\hline 0 & 1 & 0 & 0 \
\hline 0 & 0 & 1 & 1 \
\hline 0 & 0 & 1 & 0 \
\hline 0 & 0 & 0 & 1 \
\hline 0 & 0 & 0 & 0\\hline
\end{array}$ 
Complete truth tables for each of the following propositions.
-(?X • Y) ? (X • Y)

Accepted Answer

The answer of Note: the solutions to most of the...

Question 19

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment.
For exercises with only one propositional variable, the standard assignment is:
 $\begin{array} {| l | }
\hline  \alpha\\hline \text {1 }\\hline \text {0 }\\hline
\end{array}$
 
For exercises with two propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | } 
\hline \mathbf { n } & \boldsymbol { \beta } \
\hline 1 & 1 \
\hline 1 & 0 \
\hline 0 & 1 \
\hline 0 & 0 \
\hline
\end{array}$$ 
For exercises with three propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | c | } 
\hline \alpha & \beta & \gamma \
\hline 1 & 1 & 1 \
\hline 1 & 1 & 0 \
\hline 1 & 0 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 1 & 0 \
\hline 0& 0 & 1 \
\hline 0 & 0 &0\
\hline
\end{array}$$ 
For exercises with four propositional variables, the standard assignment is:
 $\begin{array}{|c|c|c|c|}
\hline\alpha & \beta & \gamma & \delta \
\hline 1 & 1 & 1 & 1 \
\hline 1 & 1 & 1 & 0 \
\hline 1 & 1 & 0 & 1 \
\hline 1 & 1 & 0 & 0\
\hline 1 & 0 & 1 & 1 \
\hline 1 & 0 & 1 & 0 \
\hline 1 & 0 & 0 & 1 \
\hline 1 & 0 & 0 & 0 \
\hline 0 & 1 & 1 & 1 \
\hline 0 & 1 & 1 & 0 \
\hline 0 & 1 & 0 & 1\
\hline 0 & 1 & 0 & 0 \
\hline 0 & 0 & 1 & 1 \
\hline 0 & 0 & 1 & 0 \
\hline 0 & 0 & 0 & 1 \
\hline 0 & 0 & 0 & 0\\hline
\end{array}$ 
Complete truth tables for each of the following propositions.
-A ? [(?B $ \lor $ A) ? ?A]

Accepted Answer

The answer of Note: the solutions to most of the...

Question 20

Note: the solutions to most of the multiple choice questions in these sections use what call the standard assignment of truth values to atomic propositions. The standard assignment of truth values assigns the values given here to the variables in the wffs in the exercises, when read left to right. So, the first variable in the formula read left to right gets the α assignment; the second variable in the formula read left to right (if any) gets the β assignment; the third variable in the formula read left to right (if any) gets the γ assignment; and the fourth variable in the formula read left to right (if any) gets the δ assignment.
For exercises with only one propositional variable, the standard assignment is:
 $\begin{array} {| l | }
\hline  \alpha\\hline \text {1 }\\hline \text {0 }\\hline
\end{array}$
 
For exercises with two propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | } 
\hline \mathbf { n } & \boldsymbol { \beta } \
\hline 1 & 1 \
\hline 1 & 0 \
\hline 0 & 1 \
\hline 0 & 0 \
\hline
\end{array}$$ 
For exercises with three propositional variables, the standard assignment is:
 $$\begin{array} { | c | c | c | } 
\hline \alpha & \beta & \gamma \
\hline 1 & 1 & 1 \
\hline 1 & 1 & 0 \
\hline 1 & 0 & 1 \
\hline 1 & 0 & 0 \
\hline 0 & 1 & 1 \
\hline 0 & 1 & 0 \
\hline 0& 0 & 1 \
\hline 0 & 0 &0\
\hline
\end{array}$$ 
For exercises with four propositional variables, the standard assignment is:
 $\begin{array}{|c|c|c|c|}
\hline\alpha & \beta & \gamma & \delta \
\hline 1 & 1 & 1 & 1 \
\hline 1 & 1 & 1 & 0 \
\hline 1 & 1 & 0 & 1 \
\hline 1 & 1 & 0 & 0\
\hline 1 & 0 & 1 & 1 \
\hline 1 & 0 & 1 & 0 \
\hline 1 & 0 & 0 & 1 \
\hline 1 & 0 & 0 & 0 \
\hline 0 & 1 & 1 & 1 \
\hline 0 & 1 & 1 & 0 \
\hline 0 & 1 & 0 & 1\
\hline 0 & 1 & 0 & 0 \
\hline 0 & 0 & 1 & 1 \
\hline 0 & 0 & 1 & 0 \
\hline 0 & 0 & 0 & 1 \
\hline 0 & 0 & 0 & 0\\hline
\end{array}$ 
Complete truth tables for each of the following propositions.
-(?C ? ?D) ? [D ? (C ? D)]

Accepted Answer

The answer of Note: the solutions to most of the...

Quiz 2: Propositional Logic: Syntax and Semantic

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(∼P ⊃ P) $\lor$ (A ⊃ P)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(∼P ⊃ P) $\lor$ (P ⊃ A)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -∼(Q ⊃ C) $\lor$ (Z • ∼X)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -∼[(Z ⊃ B) • (P ⊃ C)] $\lor$ [(X • Y) ≡ A]

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(P ⊃ ∼Q) $\lor$ ∼P

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(P ≡ Q) $\lor$ (P ≡ ∼Q)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P $\lor$ Q) ⊃ X] ≡ ∼(P $\lor$ Q)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P • Q) $\lor$ (∼P • Q)] $\lor$ [(P • ∼Q) $\lor$ (∼P • ∼Q)]

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -∼[(A ⊃ P) $\lor$ (A ⊃ Q)] • (P • Q)

Quiz 2: Propositional Logic: Syntax and Semantic

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(∼P ⊃ P) ∨ \lor ∨ (A ⊃ P)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(∼P ⊃ P) ∨ \lor ∨ (P ⊃ A)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -∼(Q ⊃ C) ∨ \lor ∨ (Z • ∼X)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -∼[(Z ⊃ B) • (P ⊃ C)] ∨ \lor ∨ [(X • Y) ≡ A]

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(P ⊃ ∼Q) ∨ \lor ∨ ∼P

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(P ≡ Q) ∨ \lor ∨ (P ≡ ∼Q)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P ∨ \lor ∨ Q) ⊃ X] ≡ ∼(P ∨ \lor ∨ Q)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P • Q) ∨ \lor ∨ (∼P • Q)] ∨ \lor ∨ [(P • ∼Q) ∨ \lor ∨ (∼P • ∼Q)]

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -∼[(A ⊃ P) ∨ \lor ∨ (A ⊃ Q)] • (P • Q)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(∼P ⊃ P) $\lor$ (A ⊃ P)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(∼P ⊃ P) $\lor$ (P ⊃ A)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -∼(Q ⊃ C) $\lor$ (Z • ∼X)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -∼[(Z ⊃ B) • (P ⊃ C)] $\lor$ [(X • Y) ≡ A]

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(P ⊃ ∼Q) $\lor$ ∼P

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -(P ≡ Q) $\lor$ (P ≡ ∼Q)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P $\lor$ Q) ⊃ X] ≡ ∼(P $\lor$ Q)

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -[(P • Q) $\lor$ (∼P • Q)] $\lor$ [(P • ∼Q) $\lor$ (∼P • ∼Q)]

Assume A, B, C are true; X, Y, Z are false; and P and Q are unknown. Evaluate the truth value of each complex expression. -∼[(A ⊃ P) $\lor$ (A ⊃ Q)] • (P • Q)