ðŸŠī Notes

Induction

1 min read

Course: CSCI 1900

Argument Validity

  • What does it mean for an argument to be valid?
    • An argument is valid if its conclusion must be true when the premises are true

Validity from Tautologies

  • Modus Ponens → if 𝑝→𝑞 is true, and 𝑝 is true, then 𝑞 must be true
  • Modus Tollens → if 𝑝→𝑞 and 𝑞 is false, then 𝑝 must be false
  • Disjunctive Syllogism → if 𝑝âˆĻ𝑞 is true, and 𝑝 is false, then 𝑞 is true
  • Transitivity of Implication → if 𝑝→𝑞 and 𝑞→𝑟, then 𝑝→𝑟
  • (and many more)

Valid Argument

  • Premise 1 → if it is raining, then the ground is wet
  • Premise 2 → it is raining
  • Conclusion → the ground is wet

Invalid Argument

  • Premise 1 → if it is raining, then the ground is wet
  • Premise 2 → the ground is wet
  • Conclusion → it is raining

Graph View

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