### myCBSEguide App

Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

Install Now**Relations and Functions class 12 Notes Mathematics** in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Relations and Functions class 12 Notes latest chapter wise notes for quick preparation of CBSE board exams and school-based annual examinations. Class 12 Mathematics notes on chapter 1 Relations and Functions are also available for download in CBSE Guide website.

## Relations and Functions Class 12 Notes Mathematics

Download CBSE class 12th revision notes for chapter 1 Relations and Functions in PDF format for free. Download revision notes for Relations and Functions class 12 Notes and score high in exams. These are the Relations and Functions class 12 Notes prepared by team of expert teachers. The revision notes help you revise the whole chapter 1 in minutes. Revision notes in exam days is one of the best tips recommended by teachers during exam days.

**Download Revision Notes as PDF**

**CBSE Class 12 Mathematics Chapter 1 Relations and Functions**

**TYPES OF RELATIONS:**

**Empty Relation**: It is the relation R in X given by R = .**Universal Relation**: It is the relation R in X given by R = .**Reflexive Relation**: A relation R in a set A is called reflexive if (a, a) ∈ R for every a ∈ A.**Symmetric Relation**: A relation R in a set A is called symmetric if (, ) ∈ R implies that (, ) ∈ R, for all , ∈**Transitive Relation**: A relation R in a set A is called transitive if (, ) ∈ R, and (, ) ∈ R together imply that all , , ∈ A.**EQUIVALENCE RELATION:**A relation R in a set A is said to be an equivalence relation if R is reflexive, symmetric and transitive.**Equivalence Classes:**Every arbitrary equivalence relation R in a set X divides X into mutually disjoint subsets (Ai) called partitions or subdivisions of X satisfying the following conditions:

All elements of Ai are related to each other for all i.

No element of Ai is related to any element of Aj whenever i ≠ j

· . These subsets () are called equivalence classes.

· For an equivalence relation in a set X, the equivalence class containing a ∈ X, denoted by [a], is the subset of X containing all elements b related to a.

****Function: A relation f: A** B is said to be a function if every clement of A is correlated to a

Unique element in B.

***A is domain **

*** B is codomain **

- A
**function**: X Y is**one-one**(or**injective**), if . - A
**function**: X Y is**onto**(or**surjective**), if such that - A
**function**: X Y is**one-one-onto**(or**bijective**), if is both one-one and onto. **The composition of function**: A B and : B C is the function given by- A
**function**: X Y is**invertible**, if such that and - A
**function**: X Y is**invertible**, if and only if is one-one and onto. **Given a finite set X, a function**: X X is one-one (respectively onto) if and only if is onto (respectively one-one). This is the characteristics property of a finite set. This is not true for infinite set.**A binary function*** on A is a function * from A x A to A.**An element**: is the identity element for binary operation * , if**An element****is invertibel for binary operation ***: if there exists such that where is the binary identity for the binary operation *. The element is called the inverse of and is denoted by .- An operation * on X is
**commutative**, if in X. - An operation * on X is
**associative**, if in X.

**CBSE Class 12 Revision Notes and Key Points**

Relations and Functions class 12 Notes Mathematics. CBSE quick revision note for class-12 Chemistry Physics Math’s, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do if for you. These notes will certainly save your time during stressful exam days.

- Physics
- Chemistry
- Mathematics
- Biology
- Accountancy
- Economics
- Business Studies
- Computer Science
- Informatics Practices
- English Core
- History
- Physical Education

To download Relations and Functions class 12 Notes Mathematics, sample paper for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT Relations and Functions, NCERT Exemplar Relations and Functions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through **the best app for CBSE students** and myCBSEguide website

- Trigonometric Functions class 12 Notes Mathematics
- Matrices class 12 Notes Mathematics
- Determinants class 12 Notes Mathematics
- Continuity and Differentiability class 12 Notes Mathematics
- Application of Derivatives class 12 Notes Mathematics
- Integrals class 12 Notes Mathematics
- Application of Integrals class 12 Notes Mathematics
- Differential Equations class 12 Notes Mathematics
- Vector Algebra class 12 Notes Mathematics
- Three Dimensional Geometry class 12 Notes Mathematics
- Linear Programming class 12 Notes Mathematics
- Probability class 12 Notes Mathematics

### Test Generator

Create question paper PDF and online tests with your own name & logo in minutes.

Create Now### myCBSEguide

Question Bank, Mock Tests, Exam Papers, NCERT Solutions, Sample Papers, Notes

Install Now