Abstract
P | Q | P→Q | ¬P∨Q |
---|
0 | 0 | 1 | 1 |
0 | 1 | 1 | 1 |
1 | 0 | 0 | 0 |
1 | 1 | 1 | 1 |
Hypothesis
- Also known as Antecedent
- The part after
if
Conclusion
- Also known as Consequent
- The part after
then
Bi-conditional
- Represented with ↔
- P↔Q means P is true
if AND only if
Q
Sufficient Condition
- Given P→Q
- P is a a sufficient condition for Q
- If P is true, Q is definitely true
Necessary Condition
- Given P→Q
- Q is a necessary condition for P
- Q must be true in order for P to be claimed true
Vacuously True
- True by default
- When the Hypothesis is false, then statement as a whole is said to be true regardless of whether the Conclusion is true of false
Implication Law
P→Q≡¬P∨Q
Useful when we need to perform Proof by Contradiction (反证法) on Conditional Statement
3 Variants
Converse (相反)
Q→P
Inverse (对立)
¬P→¬Q
P | Q | ¬P | ¬Q | ¬P→¬Q |
---|
0 | 0 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 0 | 1 |
Contrapositive (逆否命题)
¬Q→¬P
Q | P | ¬Q | ¬P | ¬Q→¬P |
---|
0 | 0 | 1 | 1 | 1 |
1 | 0 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 1 |