Discrete Mathematics - Vol 1 | 4. Rules of Inference by Abraham | Learn Smarter
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Knowledge
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.

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Sections

  • 4

    Rules Of Inference

    This section introduces rules of inference in propositional logic, detailing how valid arguments can be formed and analyzed.

    Learning Practice

  • 4.1.1

    Valid Arguments In Propositional Logic

    This section introduces valid arguments in propositional logic, explaining the structure, verification processes, and common forms of inference used to determine argument validity.

    Learning Practice

  • 4.1.2

    Abstract Argument Form

    This section introduces valid argument forms in propositional logic, explaining how to evaluate arguments through premises and conclusions.

    Learning Practice

  • 4.1.3

    Checking Validity Of Argument Forms

    This section discusses the validity of argument forms in propositional logic, introducing the rules of inference and common fallacies.

    Learning Practice

  • 4.1.4

    Rules Of Inference

    The section explores the validity of arguments in propositional logic using rules of inference and identifies common logical fallacies.

    Learning Practice

  • 4.1.4.1

    Modus Ponens

    This section focuses on the rule of inference known as Modus Ponens, illustrating its structure and validity in propositional logic.

    Learning Practice

  • 4.1.4.2

    Modus Tollens

    This section introduces Modus Tollens, a rule of inference used to derive conclusions from given premises in propositional logic.

    Learning Practice

  • 4.1.4.3

    Transitive Law (Hypothetical Syllogism)

    This section introduces the transitive law, or hypothetical syllogism, which states that if p implies q and q implies r, then p implies r.

    Learning Practice

  • 4.1.4.4

    Disjunctive Syllogism

    Disjunctive Syllogism is a rule of inference that allows one to deduce a conclusion from a disjunction and the negation of one of its disjuncts.

    Learning Practice

  • 4.1.4.5

    Addition Law

    This section introduces the concept of valid arguments in propositional logic and the role of rules of inference in establishing their validity.

    Learning Practice

  • 4.1.4.6

    Simplification Law

    The Simplification Law outlines how to validate logical arguments using rules of inference and their application in propositional logic.

    Learning Practice

  • 4.1.5

    Verifying Complex Arguments With Rules Of Inference

    This section introduces the concept of valid arguments in propositional logic, focusing on rules of inference that help verify the correctness of complex arguments.

    Learning Practice

  • 4.1.6

    Fallacies

    This section introduces logical fallacies that may appear valid at first glance but are actually incorrect.

    Learning Practice

  • 4.1.6.1

    Fallacy Of Affirming The Conclusion

    The fallacy of affirming the conclusion arises when the conclusion of an argument is incorrectly assumed to be true based on the premises, leading to invalid reasoning.

    Learning Practice

  • 4.1.6.2

    Fallacy Of Denying The Hypothesis

    The section discusses the fallacy of denying the hypothesis, which involves incorrectly concluding a negation based on a premise and its negation.

    Learning Practice

  • 4.2

    Summary

    This section introduces valid arguments in propositional logic and explores rules of inference and common logical fallacies.

    Learning Practice

References

ch4.pdf

Class Notes

Memorization

What we have learnt

  • Understanding valid argumen...
  • Rules of inference serve as...
  • Complex argument forms can ...

Final Test

Revision Tests