Relationships in Truth Statements
Exercise
Answers
- Contingent
| A |
B |
A ⊃ (A ⋅ B) |
| T |
T |
T T
|
| T |
F |
F F
|
| F |
T |
T F
|
| F |
F |
T F
|
- Tautology
| A |
B |
(A ⋅ B) ⊃ (~A ⊃ ~B) |
| T |
T |
T T T
|
| T |
F |
F T T
|
| F |
T |
F T F
|
| F |
F |
F T T
|
- Tautology
| A |
B |
(A ⋅ ~A) ⊃ B |
| T |
T |
F T T
|
| T |
F |
F T F
|
| F |
T |
F T T
|
| F |
F |
F T F
|
- Contingent
| A |
B |
(A ⊃ A) ⊃ (B ⋅ ~B) |
| T |
T |
T F F
|
| T |
F |
T F F
|
| F |
T |
T F F
|
| F |
F |
T F F
|
- Tautology
| A |
B |
(A ⋅ B) ⊃ (A v B) |
| T |
T |
T T T
|
| T |
F |
F T T
|
| F |
T |
F T T
|
| F |
F |
F T F
|
- Contingent
| A |
B |
(A v B) ⊃ (A ⋅ B) |
| T |
T |
T T T
|
| T |
F |
T F F
|
| F |
T |
T F F
|
| F |
F |
F T F
|
- Contingent
| A |
B |
(~A ⊃ ~B) ⊃ (~B ⊃ ~A) |
| T |
T |
T T T
|
| T |
F |
F F F
|
| F |
T |
F T T
|
| F |
F |
T T T
|
- Tautology
| A |
B |
(A ⊃ B) ⊃ (~B ⊃ ~A) |
| T |
T |
T T T
|
| T |
F |
F T F
|
| F |
T |
T T T
|
| F |
F |
T T T
|
- Contingent
| A |
B |
(B v ~B) ⊃ A |
| T |
T |
T T
|
| T |
F |
T T
|
| F |
T |
T F
|
| F |
F |
T F
|
- Tautology
| A |
B |
(A v B) v ~A |
| T |
T |
T T F
|
| T |
F |
T T F
|
| F |
T |
T T T
|
| F |
F |
F T T
|