Discrete Mathematics - Vol 1 | 21. Equivalence Relation 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
21. Equivalence Relation

The lecture introduces the concept of equivalence relations, which are defined by three main properties: reflexivity, symmetry, and transitivity. An example is given with integer congruences, showing how these properties apply. The discussion extends to equivalence classes, highlighting their formation and uniqueness, as well as the notable property that equivalence classes are either completely disjoint or identical.

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

  • 21

    Equivalence Relation

    An equivalence relation is a specific type of relation over a set that satisfies properties of reflexivity, symmetry, and transitivity.

    Learning Practice

  • 21.1

    Definition Of Equivalence Relation

    This section introduces equivalence relations, detailing their properties—reflexivity, symmetry, and transitivity—and explains equivalence classes through examples involving modulo operations.

    Learning Practice

  • 21.2

    Example Of An Equivalence Relation

    This section introduces equivalence relations and their defining properties: reflexivity, symmetry, and transitivity.

    Learning Practice

  • 21.3

    Properties Of Equivalence Relations

    This section introduces equivalence relations, which must be reflexive, symmetric, and transitive, and explains equivalence classes with examples.

    Learning Practice

  • 21.4

    Equivalence Classes

    This section introduces equivalence relations and equivalence classes, explaining their definitions and properties through examples, particularly in integer congruences.

    Learning Practice

  • 21.5

    Examples Of Equivalence Classes

    This section explores equivalence classes defined by equivalence relations, demonstrating their properties and providing practical examples using modulo arithmetic.

    Learning Practice

  • 21.6

    Disjoint Equivalence Classes

    This section introduces the concept of equivalence relations and equivalence classes, emphasizing their properties and significance in set theory.

    Learning Practice

  • 21.7

    Implication Of Equivalence Classes

    This section introduces equivalence relations and equivalence classes, highlighting their definitions and properties.

    Learning Practice

  • 21.8

    Theorem On Equivalence Classes

    This section introduces equivalence relations and classes, explaining their properties and significance in mathematics using integer modulo operations.

    Learning Practice

References

ch21.pdf

Class Notes

Memorization

What we have learnt

  • Equivalence relations requi...
  • An equivalence class is a s...
  • Equivalence classes derived...

Final Test

Revision Tests