Discrete Mathematics - Vol 1 | 18. Operations on Relations by Abraham | Learn Smarter
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18. Operations on Relations

The chapter discusses operations on relations, including set-theoretic operations such as union, intersection, and composition. It explores the concepts of powers of relations and various closure properties, including reflexive, symmetric, and transitive closures. Through examples, it illustrates how relations can be manipulated and expanded to satisfy specific properties.

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Sections

  • 18

    Operations On Relations

    This section covers operations on relations in discrete mathematics, including union, intersection, and composition of relations.

    Learning Practice

  • 18.1

    Union Of Relations

    This section discusses the operations on relations, focusing on union, intersection, and closure concepts in the context of discrete mathematics.

    Learning Practice

  • 18.2

    Intersection Of Relations

    This section explores set-theoretic operations on relations, including union, intersection, differences, powers, and closures.

    Learning Practice

  • 18.3

    Difference Of Relations

    This section explains the operations that can be performed on mathematical relations, specifically focusing on the difference, intersection, and union of relations.

    Learning Practice

  • 18.4

    Composition Of Relations

    This section discusses important operations on relations including set operations (union, intersection, difference) and introduces the concepts of composition of relations and their powers.

    Learning Practice

  • 18.5

    Powers Of A Relation

    This section discusses the powers of a relation and operations that can be performed on relations, including union, intersection, and composition.

    Learning Practice

  • 18.6

    Interpretation Of Powers Of Relation

    This section discusses the operations on relations, focusing on the powers of a relation and how they can be interpreted in a graph context.

    Learning Practice

  • 18.7

    Closure Of A Relation

    This section explores the closure of a relation with respect to a certain property, detailing how to minimally expand a relation to satisfy given properties such as reflexivity, symmetry, and transitivity.

    Learning Practice

  • 18.7.1

    Reflexive Closure

    This section discusses reflexive closure in relation to set operations, particularly focusing on how to ensure a relation includes all pairs of the form (a, a) for elements in a set.

    Learning Practice

  • 18.7.2

    Symmetric Closure

    This section discusses the concept of symmetric closure of a relation in discrete mathematics.

    Learning Practice

  • 18.7.3

    Transitive Closure

    This section introduces the concept of transitive closure of a relation and explains its significance in formal mathematics.

    Learning Practice

References

ch17.pdf

Class Notes

Memorization

What we have learnt

  • Relations can undergo set-t...
  • The composition of relation...
  • Closure of a relation refer...

Final Test

Revision Tests