Logic Tautology, Contradiction, Contingency YouTube Lecture Handouts

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Tautology, Contradiction, Contingency|Statement Forms in Logic

Logic Tautology, Contradiction, Contingency

Illustration: 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

Tautology ExplainedTautology Explained
P~PP ~P
TFT
FTT

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

Cases of ContingenciesCases of Contingencies
RB

validity

001
011
101
110
  • 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