Relation and function ISC Class 12 Maths ML Aggarwal Solutions

Relation and function ISC Class 12 Maths ML Aggarwal Solutions Ch-1. Step by step Solutions of ML Aggarwal ISC Class-12 Mathematics solutions of all exercise with Chapter Test Questions. Visit official Website CISCE for  detail information about ISC Board Class-12 Mathematics.

Relation and function ISC Class 12 Maths ML Aggarwal Solutions

Board	ISC
Class	12
Subject	Mathematics
Chapter-1	Relation and function
Session	2024-25
Topics	Solutions of ML Aggarwal

Relation 

The concept of relation is used in relating two objects or quantities with each other. Suppose two sets are considered. The relationship between them will be established if there is a connection between the elements of two or more non-empty sets

Types of Relations

Empty Relation: If no element of A is related to any element of A, i.e. R = φ ⊂ A × A, then the relation R in a set A is called empty relation.

Universal Relation: If each element of A is related to every element of A, i.e. R = A × A, then the relation R in set A is said to be universal relation

Reflexive- if (a, a) ∈ R, for every a ∈ A,

Symmetric- if (a₁, a₂) ∈ R implies that (a₂, a₁) ∈ R , for all a₁, a₂∈ A,

Transitive- if (a₁, a₂) ∈ R and (a₂, a₃) ∈ R  implies that (a₁, a₃) ∈ R  for all a₁, a₂, a₃ ∈ A.

Equivalence Relation- A relation R in a set A is an equivalence relation if R is reflexive, symmetric and transitive

Functions

A function is a relationship which explains that there should be only one output for each input. It is a special kind of relation(a set of ordered pairs) which obeys a rule, i.e. every y-value should be connected to only one y-value

Types of Functions

One to one Function: A function f : X → Y is defined to be one-one (or injective), if the images of distinct elements of X under f are distinct, i.e., for every x₁ , x₂ ∈ X, f(x₁ ) = f(x₂ ) implies x₁ = x₂ . Otherwise, f is called many-one

Onto Function: A function f: X → Y is said to be onto (or surjective), if every element of Y is the image of some element of X under f, i.e., for every y ∈ Y, there exists an element x in X such that f(x) = y

One-one and Onto Function: A function f: X → Y is said to be one-one and onto (or bijective), if f is both one-one and onto

Binary Operations

A binary operation ∗ on a set A is a function ∗ : A × A → A. We denote ∗ (a, b) by a ∗ b.

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Relation and function ISC Class 12 Maths ML Aggarwal Solutions Ch-1

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 ISC Class 12 Maths ML Aggarwal Solutions Ch-1

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Relation and function ISC Class 12 Maths  Ch-1

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 Class 12 Maths ML Aggarwal Solutions Ch-1

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Relation and function ML Aggarwal Solutions Ch-1

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Relation and function ISC Class 12 Maths ML Aggarwal

Ch-Test

ISC Class 12 Maths ML Aggarwal Solutions Ch-1

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