# NCERT Solutions for Class 12 Maths Chapter 1

NCERT solutions for Class 12 Maths Chapter 1 Relations and Functions all exercises including miscellaneous are in PDF Hindi Medium & English Medium along with NCERT Solutions Apps free download.

Download assignments based on Relations and functions and Previous Years Questions asked in CBSE board, important questions for practice as per latest CBSE Curriculum – 2021-2022. Download books in PDF form or buy NCERT books online.## NCERT solutions for Class 12 Maths Chapter 1

Class: 12 | Maths (English and Hindi Medium) |

Chapter 1: | Relations and Functions |

### 12th Maths Chapter 1 Solutions

NCERT solutions for Class 12 Maths Chapter 1 all exercises are given below to free download in PDF form. NCERT Books as well as Solutions are available in English and Hindi Medium. Ask your doubts related to NIOS Board and CBSE Board through Discussion Forum. NCERT Solutions and Offline apps are based on latest CBSE Syllabus.

### Class 12 Maths Chapter 1 Solutions in PDF

- Download Class 12 Maths Exercise 1.1 in PDF
- Download Class 12 Maths Exercise 1.2 in PDF
- Download Class 12 Maths Exercise 1.3 in PDF
- Download Class 12 Maths Exercise 1.4 in PDF
- Download Class 12 Maths Miscellaneous Exercise 1
- Class 12 Maths NCERT Book Chapter 1
- Class 12 Maths NCERT Book Answers
- Class 12 Maths Revision Book Chapter 1
- Class 12 Maths Revision Book Answers
- Download Class 12 Maths Assignment 1
- Download Class 12 Maths Assignment 2
- Download Class 12 Maths Assignment 2 Answers
- Download Class 12 Maths Assignment 3
- Download Class 12 Maths Assignment 4
- Class 12 Maths Solution Main Page

#### Class 12 Maths Chaper 1 Exercise 1.1 Solution in Videos

#### Class 12 Maths Chaper 1 Exercise 1.2 Solution in Videos

#### Class 12 Maths Chaper 1 Exercise 1.3 Solution in Videos

#### Class 12 Maths Chaper 1 Exercise 1.4 Solution in Videos

#### Class 12 Maths Chaper 1 Miscellaneous Exercise 1 in Videos

Before studying this lesson, you should know:

- Concept of set, types of sets, operations on sets
- Concept of ordered pair and cartesian product of set.
- Domain, co-domain and range of a relation and a function

##### Relation

Let A and B be two sets. Then a relation R from Set A into Set B is a subset of A × B.

Types of Relations

- Reflexive Relation
- Symmetric Relation
- Transitive Relation

##### Equivalence Relation

A relation R on a set A is said to be an equivalence relation on A iff

- it is reflexive
- it is symmetric
- it is transitive

###### CLASSIFICATION OF FUNCTIONS

Let f be a function from A to B. If every element of the set B is the image of at least one element of the set A i.e. if there is no unpaired element in the set B then we say that the function f maps the set A onto the set B. Otherwise we say that the function maps the set A into the set B.

Functions for which each element of the set A is mapped to a different element of the set B are said to be one-to-one.

A function can map more than one element of the set A to the same element of the set B. Such a type of function is said to be many-to-one. A function which is both one-to-one and onto is said to be a bijective function.

###### BINARY OPERATIONS

Let A, B be two non-empty sets, then a function from A × A to A is called a binary operation on A.

If a binary operation on A is denoted by *, the unique element of A associated with the ordered pair (a, b) of A × A is denoted by a * b.

The order of the elements is taken into consideration, i.e. the elements associated with the pairs (a, b) and (b, a) may be different i.e. a * b may not be equal to b * a.

Let A be a non-empty set and ‘*’ be an operation on A, then