“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 |