Logic Tautology, Contradiction, Contingency YouTube Lecture Handouts
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Tautology, Contradiction, Contingency|Statement Forms in Logic
Logic Tautology, Contradiction, Contingency
- Dogma: An example of dogma is the Ten Commandments in the Christian faith.
- Tautology or Conditional Disjunction: example double negation
- Contradiction: I respect you and I do not respect you; It is raining and it is not raining
Tautology Explained
P | ~P | P ~P |
---|---|---|
T | F | T |
F | T | T |
Indira Gandhi was assassinated or else she was not – tautology (P ~P)
Cases of Tautologies
Cases of Contradictions
- Contingency: Neither true under every possible valuation (i.e.. tautologies) nor false under every possible valuation (i.e.. contradictions)
- A contingent proposition is neither necessarily true nor necessarily false. It has some true and some false substitution instances. Example - It is raining (it can be true or false)
- If roses are red and violets are blue, then roses aren՚t red.
Cases of Contingencies
If roses are red and violets are blue then roses aren՚t red
R | B | validity |
0 | 0 | 1 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
- We can explain this only when there is if statement
- When if statement condition is true only then we will look at the condition in “then”
- If it is true then if statement is true or valid
- If I can find a single case when if condition is true but then proposition is not – then entire if then statement becomes false.
- If smoke then fire (I cannot find a single case where there is smoke and no fire and therefore it is valid)
- If fire then smoke (we can find a case of iron ball and hence invalid)
- In case of Boolean propositions – all cases can be achieved by truth table
✍ Manishika