Relations and Functions Class 12 Mathematics
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Questions and Answers

What is the concept of relation used for?

Relating two objects or quantities with each other.

Define relation mathematically.

A relation R from a set A to a set B is a subset of the cartesian product A × B obtained by describing a relationship between the first element x and the second element y of the ordered pairs in A × B.

What is an empty relation?

If no element of A is related to any element of A.

What are the extreme relations in a set A?

<p>The empty set φ and A × A.</p> Signup and view all the answers

What do students learn about in Chapter 1 of Relations and Functions for Class 12?

<p>Different types of relations and functions, the composition of functions, etc., in detail.</p> Signup and view all the answers

What is the definition of a universal relation?

<p>A relation R in a set A is a universal relation if R = A × A</p> Signup and view all the answers

Define an equivalence relation.

<p>A relation R in a set A is an equivalence relation if R is reflexive, symmetric, and transitive</p> Signup and view all the answers

What is the requirement for a function to be considered invertible?

<p>A function f : X → Y is invertible if there exists a function g : Y → X such that gof = IX and fog = IY</p> Signup and view all the answers

Explain the composition of functions.

<p>The composition of functions f and g, denoted by gof, is defined as gof (x) = g(f (x)) for every x in A</p> Signup and view all the answers

What is the definition of a binary operation on a set A?

<p>A binary operation ∗ on a set A is a function ∗ : A × A → A</p> Signup and view all the answers

Study Notes

Relations and Functions

  • The concept of relation is used to describe a connection or association between elements of two sets.

Mathematical Definition of Relation

  • A relation R from set A to set B is a subset of the Cartesian product A × B, where A × B is the set of all ordered pairs (a, b) such that a ∈ A and b ∈ B.

Empty Relation

  • An empty relation is a relation that has no elements, denoted as R = ∅.

Extreme Relations

  • In a set A, the extreme relations are:
    • The universal relation, denoted as A × A, which is the set of all ordered pairs (a, b) where a, b ∈ A.
    • The empty relation, denoted as ∅, which is the set with no ordered pairs.

Chapter 1 of Relations and Functions for Class 12

  • Students learn about the basics of relations and functions, including the definition of relations, types of relations, and operations on relations.

Universal Relation

  • A universal relation is a relation that contains all possible ordered pairs of a set A, denoted as A × A.

Equivalence Relation

  • An equivalence relation is a relation that is reflexive, symmetric, and transitive, denoting a "sameness" or "equivalence" relation between elements.

Invertible Function

  • A function is considered invertible if it is both one-to-one (injective) and onto (surjective).

Composition of Functions

  • The composition of functions f and g, denoted as (f ∘ g), is a function that combines the output of g as the input of f, resulting in a new function.

Binary Operation

  • A binary operation on a set A is a function that takes two elements of A as input and produces another element of A as output, denoted as ∘: A × A → A.

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Description

Test your knowledge of relations and functions in Class 12 Mathematics Chapter 1. This quiz covers the revision of general notation, domain, codomain, range, real-valued functions, composition of functions, and more.

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