Discrete Mathematics - Vol 1 | 6. Tutorial 1: Part I by Abraham | Learn Smarter
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6. Tutorial 1: Part I

The chapter covers the fundamentals of propositional logic, including propositional variables, logical connectives, and their representations in terms of compound propositions. It discusses the relationships among various statements through the introduction of implications such as contrapositives, converses, and inverses. Additionally, it explores how to draw truth tables to evaluate compound propositions and presents the concept of the dual of a compound proposition along with its properties.

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Sections

  • 6.1

    Discrete Mathematics

    This section introduces fundamental concepts in discrete mathematics, focusing on propositional logic, including compound propositions, truth tables, and logical connectives.

    Learning Practice

  • 6.2

    Question 1

    This section involves representing logical statements using propositional variables in discrete mathematics, focusing on implications and logical connectives.

    Learning Practice

  • 6.3

    Question 2

    This section focuses on the concepts of logical implications, specifically exploring the converse, contrapositive, and inverse of given implications.

    Learning Practice

  • 6.4

    Question 3

    This section covers constructing truth tables for compound propositions involving logical connectives.

    Learning Practice

  • 6.5

    Question 4

    This section presents propositional logic concepts and their applications in formulating compound propositions.

    Learning Practice

  • 6.6

    Question 5

    This section discusses the verification of the consistency of a system specification using propositional logic.

    Learning Practice

  • 6.6.1

    Part A

    The section focuses on basic propositional logic, specifically using variables to represent propositions and understanding their relationships through logical connectives.

    Learning Practice

  • 6.6.2

    Part B

    This section covers the basics of propositional logic, focusing on negation, implications, and constructing truth tables for compound propositions.

    Learning Practice

  • 6.7

    Question 6

    This section discusses logical equivalences and implications in propositional logic using truth tables and rules.

    Learning Practice

  • 6.7.1

    Part A

    This section covers logical propositions and implications, including methods to represent statements using propositional logic, their converses, contrapositive, and inverses.

    Learning Practice

  • 6.7.2

    Part B

    This section covers propositional logic, focusing on representing logical statements using propositional variables and identifying their forms, such as implications, converses, and contrapositives.

    Learning Practice

  • 6.8

    Question 7

    This section introduces the concept of the dual of a compound proposition in logic and provides methods for constructing and understanding duals.

    Learning Practice

  • 6.8.1

    Dual Of Compound Proposition

    This section introduces the concept of the dual of a compound proposition, explaining the transformation rules for obtaining the dual representation.

    Learning Practice

  • 6.8.2

    Constructing Duals

    This section discusses the method for constructing duals of compound propositions by interchanging conjunctions and disjunctions, along with constants.

    Learning Practice

  • 6.8.3

    Equality Of Dual And Original Statement

    This section explores the equality of dual statements and original statements in propositional logic, highlighting the necessary transformations to derive duals.

    Learning Practice

  • 6.8.4

    Duals Of Logically Equivalent Statements

    This section discusses the representation of logical statements and their duals, focusing on logically equivalent statements and their implications in discrete mathematics.

    Learning Practice

References

ch6.pdf

Class Notes

Memorization

What we have learnt

  • Propositional variables can...
  • Compound propositions can b...
  • The dual of a compound prop...

Final Test

Revision Tests