Relations and Functions: Chapter 1 Quiz
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Questions and Answers

In the context of relations, what is the definition of a universal relation?

  • A relation in a set A is called universal if it contains an infinite number of elements.
  • A relation in a set A is called universal if it contains only one element in A.
  • A relation in a set A is called universal if no element of A is related to any element of A.
  • A relation in a set A is called universal if each element of A is related to every element of A. (correct)

    • Which type of relation is defined as having no element of a set related to any other element?

  • Equivalence relation
  • Empty relation (correct)
  • Partial relation
  • Universal relation

    • What is the significance of functions in the context of relations?

  • Functions are a special kind of relation (correct)
  • Functions are subsets of relations
  • Functions are not related to relations
  • Functions have no relevance to mathematical relations

    • What is the significance of an equivalence relation in mathematics?

    <p>It plays a significant role in Mathematics</p> Signup and view all the answers

    What are the extreme types of relations based on their content?

    <p>Trivial relation and universal relation</p> Signup and view all the answers

    What is the concept of the term 'relation' in mathematics derived from?

    <p>The meaning of relation in the English language</p> Signup and view all the answers

    What do A and B represent in the given context?

    <p>Sets of students of different classes in a school</p> Signup and view all the answers

    Which example represents a relation from A to B based on the age of the students?

    <p>{(a, b) ∈ A × B: age of a is greater than age of b}</p> Signup and view all the answers

    What is the basis for determining relations from A to B according to the given context?

    <p>Familial relationships</p> Signup and view all the answers

    What does G. H. Hardy assert about mathematical beauty?

    <p>It is as elusive as any other form of beauty</p> Signup and view all the answers

    Study Notes

    Relations in Mathematics

    • A universal relation is a relation that relates every element of a set to every element of another set.

    Types of Relations

    • The empty relation is a type of relation that has no element of a set related to any other element.

    Functions and Relations

    • Functions are a type of relation where every element in the domain is related to exactly one element in the codomain.

    Equivalence Relations

    • An equivalence relation is a relation that is reflexive, symmetric, and transitive, having significance in mathematics for defining equivalence classes.

    Extreme Types of Relations

    • The two extreme types of relations based on their content are the universal relation and the empty relation.

    Origins of the Term 'Relation'

    • The concept of the term 'relation' in mathematics is derived from the everyday usage of the word, describing a connection or association between things.

    Representation in Relations

    • A and B represent two sets in a relation, where elements from set A can be related to elements from set B.

    Examples of Relations

    • The relation "is at least as old as" represents a relation from A to B based on the age of the students, where elements from set A (students) are related to elements from set B (ages).

    Basis of Relations

    • The basis for determining relations from A to B is the connection or association between the elements of the two sets.

    Mathematical Beauty

    • G. H. Hardy asserts that mathematical beauty lies in the fact that it is eternal and unchanging, and that it is not a human discovery but a reality waiting to be uncovered.

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    Description

    Test your understanding of relations and functions, domain, co-domain, and range introduced in Chapter 1.1. This quiz covers the basics of mathematical relations and functions.

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