Discrete Mathematics - Vol 1 | 8. Predicate Logic by Abraham | Learn Smarter
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8. Predicate Logic

Predicate logic enables the representation of mathematical statements that propositional logic cannot. It introduces the concept of predicates, which express properties about variables, allowing for the formulation of quantified statements. The chapter also explores two forms of quantification: universal and existential, each serving distinct roles in logical assertions.

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Sections

  • 8. 1

    Predicate Logic

    Predicate logic extends propositional logic by introducing quantifiers and predicates that can express statements about arbitrary elements.

    Learning Practice

  • 8. 1.1

    Motivation Of Studying Predicate Logic

    This section discusses the motivation for studying predicate logic, explaining its necessity for representing mathematical statements involving variables and quantifications beyond propositional logic.

    Learning Practice

  • 8. 1.2

    Representing Statements In Predicate Logic

    This section introduces predicate logic, highlighting how it represents mathematical statements through quantification.

    Learning Practice

  • 8. 1.3

    Multi-Valued Predicate Functions

    This section discusses multi-valued predicate functions, their definition, and their significance in representing mathematical statements.

    Learning Practice

  • 8. 1.4

    Converting Predicates Into Propositions

    This section elaborates on the transition from predicates to propositions in predicate logic, alongside quantification methods.

    Learning Practice

  • 8. 1.4.1

    Quantification Method

    This section introduces predicate logic, emphasizing the importance of quantification methods like universal and existential quantification.

    Learning Practice

  • 8. 1.4.2

    Universal Quantification

    This section introduces universal quantification in predicate logic, emphasizing its significance in asserting that properties hold for all elements in a domain.

    Learning Practice

  • 8. 1.4.3

    Existential Quantification

    This section introduces existential quantification as a method to express that a property holds for at least one element in a specific domain.

    Learning Practice

  • 8. 1.5

    Bounded And Free Variables

    This section introduces bounded and free variables within the context of predicate logic, explaining their significance with quantifiers.

    Learning Practice

  • 8. 1.6

    Scope Of Quantifiers

    Quantifiers in predicate logic enhance the ability to express properties over variables within a domain.

    Learning Practice

  • 8. 1.7

    Logical Equivalence In Predicate World

    This section covers the significance of logical equivalence in predicate logic, exploring the concepts of universal and existential quantification.

    Learning Practice

  • 8. 1.7.1

    De Morgan's Laws Involving Quantified Statements

    This section introduces and explains De Morgan's Laws as they relate to quantified statements in predicate logic.

    Learning Practice

  • 8. 2

    Summary

    This section explores the concept of predicate logic, emphasizing the need for predicates and quantification to express mathematical statements effectively.

    Learning Practice

References

ch8.pdf

Class Notes

Memorization

What we have learnt

  • Predicate logic extends pro...
  • Quantification methods, inc...
  • The interpretation of quant...

Final Test

Revision Tests