Discrete Mathematics - Vol 1 | 7. Tutorial 1: Part II by Abraham | Learn Smarter
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7. Tutorial 1: Part II

The chapter provides an in-depth exploration of functionally complete sets of logical operators and their properties. It allows for the representation of any compound proposition using a minimal set of logical operators, demonstrating the transformability of expressions involving implication and conjunction into solely disjunctions and negations. Furthermore, it examines satisfiability of propositions and introduces resolution methods to determine valid arguments and contradictions within logical frameworks.

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Sections

  • 7.1

    Discrete Mathematics

    This section introduces the concept of functionally complete sets of logical operators in discrete mathematics.

    Learning Practice

  • 7.1.1

    Lecture - 07

    This section explores the concept of functionally complete sets of logical operators and discusses how logical propositions can be transformed using these operators.

    Learning Practice

  • 7.1.2

    Tutorial 1: Part Ii

    This section explores functionally complete sets of logical operators and their significance in logic propositions.

    Learning Practice

  • 7.2

    Question 8

    This section explores the concept of functionally complete sets of logical operators, demonstrating how basic operators can represent complex logical propositions.

    Learning Practice

  • 7.2.1

    Functionally Complete Set Of Logical Operators

    This section discusses the concept of functionally complete sets of logical operators, demonstrating how various operators can represent all compound propositions.

    Learning Practice

  • 7.2.2

    Proving Functionality With Three Operators

    This section discusses the concept of functionally complete sets of logical operators and presents ways to prove their functionality.

    Learning Practice

  • 7.2.3

    Replacing Conjunction With Negation And Disjunction

    This section explains the process of proving that certain logical operators can represent all logical expressions.

    Learning Practice

  • 7.2.4

    Negation And Disjunction Functionality

    This section explores the functionality of negation and disjunction within propositional logic, outlining how various logical operators can represent compound propositions.

    Learning Practice

  • 7.3

    Question 9

    Question 9 discusses the concept of satisfiability in propositional logic, demonstrating how to find truth assignments that satisfy compound propositions.

    Learning Practice

  • 7.3.1

    Satisfiability Of A Compound Proposition

    This section discusses the satisfiability of compound propositions and the concept of functionally complete sets of logical operators.

    Learning Practice

  • 7.3.2

    Verification Of Other Expressions

    The section discusses the concept of functionally complete sets of logical operators and how various logical expressions can be converted or represented using basic operators.

    Learning Practice

  • 7.3.3

    Algorithm For Tautology Check

    This section discusses the algorithm to check if a compound proposition is a tautology by using the unsatisfiability of its negation.

    Learning Practice

  • 7.4

    Question 10

    This section discusses how to verify the validity of an argument using propositional logic, specifically through the application of Modus Ponens.

    Learning Practice

  • 7.4.1

    Validity Of Argument

    This section explores the validity of logical arguments, emphasizing functional completeness and satisfiability.

    Learning Practice

  • 7.5

    Question 11

    This section discusses the validity of argumentative forms in propositional logic, specifically focusing on how premises relate to conclusions.

    Learning Practice

  • 7.5.1

    Valid Argument Form For Premises

    This section explores the structure of valid arguments using logical operators and examines how premises relate to conclusions in propositional logic.

    Learning Practice

  • 7.5.2

    Tautology Implication

    This section discusses the functional completeness of logical operators and how to determine if a compound proposition is a tautology.

    Learning Practice

  • 7.6

    Question 12

    This section focuses on using resolution to determine the validity of a logical argument through propositional logic.

    Learning Practice

  • 7.6.1

    Using Resolution For Validity

    This section focuses on using resolution to establish the validity of logical propositions and explores the concept of functionally complete sets of operators.

    Learning Practice

  • 7.7

    Question 13

    This section demonstrates the use of resolution to show that a given compound proposition is unsatisfiable by constructing a resolution tree.

    Learning Practice

  • 7.7.1

    Unsatisfiability Proof Via Resolution

    This section discusses the concept of functional completeness in logical operators and proofs of satisfiability using resolution.

    Learning Practice

  • 7.8

    Final Question

    This section discusses the concept of functionally complete sets of logical operators and their role in representing compound propositions.

    Learning Practice

  • 7.8.1

    Verification Of Valid Argument

    This section covers the verification of valid arguments using logical operators and reveals how to determine the functional completeness of logical operations.

    Learning Practice

References

ch7.pdf

Class Notes

Memorization

What we have learnt

  • A set of logical operators ...
  • Implication can be expresse...
  • Resolution is a powerful me...

Final Test

Revision Tests