Discrete Mathematics - Vol 1 | 2. Logical Equivalence by Abraham | Learn Smarter
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

Typing
Memory
Math
English Adventures
Knowledge
2. Logical Equivalence

Logical equivalence is explored through the examination of propositional logic, including the definitions of tautology, contradiction, and contingency. The chapter emphasizes the significance of the contrapositive and biconditional statements and introduces standard logical identities, such as De Morgan's laws and the distributive laws. Techniques for simplifying complex logical expressions using known identities are also discussed, providing a foundation for proving logical equivalence without relying solely on truth tables.

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Sections

  • 2

    Discrete Mathematics

    This section introduces the concepts of logical equivalence, logical identities, and various properties related to propositional logic.

    Learning Practice

  • 2.1

    Logical Equivalence

    This section covers the concept of logical equivalence, including key operators, identities, tautologies, and various forms of logical statements.

    Learning Practice

  • 2.2

    Logical Operators And Propositions

    This section covers the fundamentals of logical propositions involving logical operators, logical equivalence, and key concepts like tautology, contradiction, and contingency.

    Learning Practice

  • 2.2.1

    Bi-Conditional Operator And Statement

    This section introduces the bi-conditional operator, logical equivalence, and different types of propositions such as tautologies, contradictions, and contingencies.

    Learning Practice

  • 2.2.2

    Tautology, Contradiction, And Contingency

    This section introduces the concepts of tautology, contradiction, and contingency in propositional logic.

    Learning Practice

  • 2.2.3

    Logically Equivalent Statements

    This section discusses logically equivalent statements, focusing on their definitions, truth values, and implications in propositional logic.

    Learning Practice

  • 2.3

    Standard Logical Equivalent Statements

    This section covers the concept of logical equivalence, including the identification of equivalent statements and the important logical identities that underpin these concepts.

    Learning Practice

  • 2.3.1

    Identity And Double Negation Laws

    This section covers logical equivalence and the identity laws in propositional logic, specifically focusing on tautologies, contradictions, contingencies, and how to verify logical identities through truth tables.

    Learning Practice

  • 2.3.2

    De Morgan's Law

    This section introduces De Morgan's Law, addressing logical equivalence, definitions of tautology, contradiction, and contingency, while demonstrating how to apply these concepts using truth tables.

    Learning Practice

  • 2.3.3

    Distributive Law

    The Distributive Law outlines how conjunction and disjunction can be applied together in logical expressions, demonstrating the equivalence of compound propositions.

    Learning Practice

  • 2.4

    Verification Of Logical Identities

    This section focuses on logical equivalence and identities in propositional logic, including tautologies, contradictions, and techniques for verification.

    Learning Practice

  • 2.4.1

    Truth Table Method Limitations

    This section examines the limitations of the truth table method for verifying logical equivalence, particularly concerning the number of propositional variables.

    Learning Practice

  • 2.5

    Example Of Logical Equivalence Proof

    This section explores logical equivalence, introducing key concepts like biconditional statements, tautologies, contradictions, and how to apply logical identities.

    Learning Practice

  • 2.5.1

    Using Logical Identities For Simplification

    This section discusses the use of logical equivalences and identities to simplify logical expressions in mathematical logic.

    Learning Practice

  • 2.6

    Conclusion

    This section provides a summary of key concepts regarding logical equivalence and identities in propositional logic.

    Learning Practice

  • 2.6.1

    Summary Of Concepts Introduced

    This section introduces the concept of logical equivalence in propositional logic, highlighting various logical operators and identities.

    Learning Practice

References

ch2.pdf

Class Notes

Memorization

What we have learnt

  • Logical equivalence occurs ...
  • Tautologies are statements ...
  • Standard logical identities...

Final Test

Revision Tests