Discrete Mathematics - Vol 1 | 17. Irreflexive Relation by Abraham | Learn Smarter
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17. Irreflexive Relation

The chapter delves into various types of binary relations, including irreflexive, symmetric, asymmetric, antisymmetric, and transitive relations, outlining their definitions and characteristics. It also discusses matrices representing these relations and explores their implications in terms of directed graphs. Moreover, the chapter emphasizes the distinctions and potential overlaps between reflexivity and irreflexivity, as well as the absence of direct relationships among symmetric, asymmetric, and antisymmetric properties.

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Sections

  • 17.1

    Irreflexive Relation

    An irreflexive relation is defined as a relation in which no element in a set A is related to itself.

    Learning Practice

  • 17.1.1

    Definition And Characteristics

    This section defines various types of relations, including irreflexive, symmetric, asymmetric, antisymmetric, and transitive relations, along with their characteristics.

    Learning Practice

  • 17.1.2

    Examples Of Irreflexive Relations

    This section introduces irreflexive relations, explaining that no element can relate to itself within such relations.

    Learning Practice

  • 17.1.3

    Reflexive And Irreflexive Relations

    This section discusses reflexive and irreflexive relations, detailing their definitions, properties, and examples.

    Learning Practice

  • 17.2

    Symmetric Relations

    This section defines and examines symmetric relations, their properties, and their implications in the context of sets.

    Learning Practice

  • 17.2.1

    Definition And Characteristics

    This section defines various types of relations, focusing on irreflexive, symmetric, asymmetric, antisymmetric, and transitive relations.

    Learning Practice

  • 17.2.2

    Examples Of Symmetric Relations

    This section defines symmetric relations, explaining their properties, examples, and relationships with other types of relations.

    Learning Practice

  • 17.2.3

    Reflexive Vs. Symmetric Relations

    This section introduces various types of binary relations, including irreflexive, symmetric, asymmetric, and antisymmetric relations, highlighting their definitions and properties.

    Learning Practice

  • 17.3

    Asymmetric Relations

    The section explores asymmetric relations, their properties, and their distinction from other types of relations in set theory.

    Learning Practice

  • 17.3.1

    Definition And Characteristics

    This section discusses various types of relations defined from a set to itself, such as irreflexive, symmetric, asymmetric, and antisymmetric relations, including their characteristics and examples.

    Learning Practice

  • 17.3.2

    Examples Of Asymmetric Relations

    This section explores the concept of asymmetric relations and their characteristics, including related definitions and examples.

    Learning Practice

  • 17.4

    Antisymmetric Relations

    This section introduces antisymmetric relations, explaining their definition, properties, and significance within the context of binary relations.

    Learning Practice

  • 17.4.1

    Definition And Characteristics

    This section defines various types of relations, focusing on irreflexive, symmetric, asymmetric, antisymmetric, and transitive relations, highlighting their properties and examples.

    Learning Practice

  • 17.4.2

    Examples Of Antisymmetric Relations

    This section discusses antisymmetric relations, illustrating their properties through examples and definitions.

    Learning Practice

  • 17.5

    Transitive Relations

    This section defines various types of binary relations, focusing on transitive relations and their properties.

    Learning Practice

  • 17.5.1

    Definition And Characteristics

    This section defines and explains key properties of specific relations such as irreflexive, symmetric, asymmetric, antisymmetric, and transitive relations.

    Learning Practice

  • 17.5.2

    Examples Of Transitive Relations

    This section explores the concepts of irreflexive, symmetric, asymmetric, antisymmetric, and transitive relations, providing examples and clarifications.

    Learning Practice

  • 17.6

    Summary Of Binary Relations

    This section defines various special binary relations such as irreflexive, symmetric, asymmetric, antisymmetric, and transitive relations.

    Learning Practice

References

ch16 - part B.pdf

Class Notes

Memorization

What we have learnt

  • Irreflexive relations do no...
  • Symmetric relations require...
  • Antisymmetric relations all...

Final Test

Revision Tests