Summary
Modus ponens
| Premise 1: | Premise 2: | Conclusion: | ||
|---|---|---|---|---|
| T | T | T | T | T |
| T | F | F | T | |
| F | T | T | F | |
| F | F | T | F |
Modus tollens
| Premise 1: | Premise 2: | Conclusion: | ||
|---|---|---|---|---|
| T | T | T | F | |
| T | F | F | T | |
| F | T | T | F | |
| F | F | T | T | T |
Generalisation
Either or
| Premise: | Conclusion: | ||
|---|---|---|---|
| T | T | T | T |
| T | F | T | T |
| F | T | F | |
| F | F | F |
Specialisation
Discard extra info
| Premise: | Conclusion: | ||
|---|---|---|---|
| T | T | T | T |
| T | F | F | |
| F | T | F | |
| F | F | F |
Conjunction
If both premises are true, their conjuction is true
| Conclusion: | ||
|---|---|---|
| T | T | T |
| T | F | |
| F | T | |
| F | F |
Elimination
Ruling out one possibility
| Premise 1: | Premise 2: | Conclusion: | ||
|---|---|---|---|---|
| T | T | T | F | |
| T | F | T | T | T |
| F | T | T | F | |
| F | F | F | T |
Transitivity
When
| Premise 1: | Premise 2: | Conclusion: | |||
|---|---|---|---|---|---|
| T | T | T | T | T | T |
| T | T | F | T | F | |
| T | F | T | F | T | |
| T | F | F | F | T | |
| F | T | T | T | T | T |
| F | T | F | T | F | |
| F | F | T | T | T | T |
| F | F | F | T | T | T |
Proof by division into cases
If at least one of the cases is true, and all cases leads to a certain conclusion, then the conclusion is also true
| Premise 1: | Premise 2: | Premise 3: | Conclusion: | |||
|---|---|---|---|---|---|---|
| T | T | T | T | T | T | T |
| T | T | F | T | F | F | |
| T | F | T | T | T | T | T |
| T | F | F | T | F | T | |
| F | T | T | T | T | T | T |
| F | T | F | T | T | F | |
| F | F | T | F | T | T | |
| F | F | F | F | T | T |
Contradiction rule
If not
| Premise: | Conclusion: | |
|---|---|---|
| T | T | T |
| F | F |