Symbolic Logic 5E: 2.4, I

“Use truth tables to characterize the following statement forms as tautologous, contradictory, or contingent”

1. Contingent.

P

¬P

P→¬P

T

F

F

F

T

T

2. Contradiction.

P

¬P

P→¬P

¬P→P

(¬P→P) ∧ (¬P→P)

T

F

F

T

F

F

T

T

F

F

3. Tautology.

P

(P→P)

P→(P→P)

T

T

T

F

T

T

4. Contingent.

P

(P→P)

(P→P)→P

T

T

T

F

T

F

5. Tautology.

P

P ∧ P

P→(P ∧ P)

T

T

T

F

F

T

6. Tautology.

P

Q

P ∧ Q

(P ∧ Q)→P

T

T

T

T

T

F

F

T

F

T

F

T

F

F

F

T

7. Tautology.

P

Q

R

P→Q

R ∧ P

¬(R ∧ P)

Q ∧ R

¬(Q ∧ R)

¬(Q ∧ R)→¬(R ∧ P)

(P→Q)→[¬(Q ∧ R)→¬(R ∧ P)]

T

T

T

T

T

F

T

F

T

T

T

T

F

T

F

T

F

T

T

T

T

F

F

F

F

T

F

T

T

T

T

F

T

F

T

F

F

T

F

T

F

F

F

T

F

T

F

T

T

T

F

F

T

T

F

T

F

T

T

T

F

T

T

T

F

T

T

F

T

T

F

T

F

T

F

T

F

T

T

T

8. Contradiction.

P

Q

¬P

¬P ∧ Q

Q→P

(¬P ∧ Q) ∧ (Q→P)

T

T

F

F

T

F

T

F

F

F

T

F

F

F

T

F

T

F

F

T

T

T

F

F

9. Contingent.

P

Q

P→Q

(P→Q)→Q

[(P→Q)→Q]→Q

T

T

T

T

T

T

F

F

T

F

F

F

T

F

T

F

T

T

T

T

10. Tautology.

P

Q

P→Q

(P→Q)→P

[(P→Q)→P]→P

T

T

T

T

T

T

F

F

F

T

F

F

T

F

T

F

T

T

F

T

 

 

 

 

 

 

 

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