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 (a_{1}, a_{2}) ∈ R implies that (a_{2}, a_{1}) ∈ R , for all a_{1}, a_{2}∈ A,

**Transitive- **if (a_{1}, a_{2}) ∈ R and (a_{2}, a_{3}) ∈ R implies that (a_{1}, a_{3}) ∈ R for all a_{1}, a_{2}, a_{3} ∈ 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 x_{1} , x_{2} ∈ X, f(x_{1} ) = f(x_{2} ) implies x_{1} = x_{2} . 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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### Ch-Test

ISC Class 12 Maths ML Aggarwal Solutions Ch-1

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