4. Rules of Inference - Discrete Mathematics - Vol 1
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4. Rules of Inference

4. Rules of Inference

The lecture on rules of inference covers valid arguments in propositional logic, highlighting the structure of arguments and the significance of argument forms. It explains the concepts of premises and conclusions, the verification of argument validity through tautologies, and introduces rules of inference for simplifying complex arguments. Common fallacies in reasoning are also discussed to clarify misunderstandings in logical arguments.

16 sections

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Sections

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  1. 4
    Rules Of Inference

    This section introduces rules of inference in propositional logic, detailing...

  2. 4.1.1
    Valid Arguments In Propositional Logic

    This section introduces valid arguments in propositional logic, explaining...

  3. 4.1.2
    Abstract Argument Form

    This section introduces valid argument forms in propositional logic,...

  4. 4.1.3
    Checking Validity Of Argument Forms

    This section discusses the validity of argument forms in propositional...

  5. 4.1.4
    Rules Of Inference

    The section explores the validity of arguments in propositional logic using...

  6. 4.1.4.1
    Modus Ponens

    This section focuses on the rule of inference known as Modus Ponens,...

  7. 4.1.4.2
    Modus Tollens

    This section introduces Modus Tollens, a rule of inference used to derive...

  8. 4.1.4.3
    Transitive Law (Hypothetical Syllogism)

    This section introduces the transitive law, or hypothetical syllogism, which...

  9. 4.1.4.4
    Disjunctive Syllogism

    Disjunctive Syllogism is a rule of inference that allows one to deduce a...

  10. 4.1.4.5
    Addition Law

    This section introduces the concept of valid arguments in propositional...

  11. 4.1.4.6
    Simplification Law

    The Simplification Law outlines how to validate logical arguments using...

  12. 4.1.5
    Verifying Complex Arguments With Rules Of Inference

    This section introduces the concept of valid arguments in propositional...

  13. 4.1.6

    This section introduces logical fallacies that may appear valid at first...

  14. 4.1.6.1
    Fallacy Of Affirming The Conclusion

    The fallacy of affirming the conclusion arises when the conclusion of an...

  15. 4.1.6.2
    Fallacy Of Denying The Hypothesis

    The section discusses the fallacy of denying the hypothesis, which involves...

  16. 4.2

    This section introduces valid arguments in propositional logic and explores...

What we have learnt

  • Understanding valid arguments involves determining if the premises imply the conclusion as a tautology.
  • Rules of inference serve as building blocks for proving the validity of larger arguments without constructing truth tables.
  • Complex argument forms can be broken down into simpler components, allowing for the verification of their validity using established rules.

Key Concepts

-- Valid Argument
An argument is considered valid if the conjunction of its premises implies its conclusion as a tautology.
-- Rules of Inference
Logical tools that allow for the derivation of new conclusions from established premises.
-- Tautology
A statement that is true in all possible scenarios.
-- Modus Ponens
A rule stating that if 'p' is true and 'p implies q' is true, then 'q' is also true.
-- Fallacy of Affirming the Conclusion
An invalid argument form that mistakenly concludes 'p' from 'p implies q' and 'q'.
-- Fallacy of Denying the Hypothesis
An invalid argument form that incorrectly concludes '¬q' from 'p implies q' and '¬p'.

Additional Learning Materials

Supplementary resources to enhance your learning experience.