# NCERT Solutions for Class 12 Maths Chapter 1 – Relations and Functions

Instasolv’s NCERT Solutions for Class 12 Maths Chapter 1- Relations and Functions** **drafted meticulously by our team of experts with years of training at disposal, makes sure to enable you to grasp the intricate concepts of** **the chapter**. **They provide step by step solutions to all the questions of all the 4 exercises in the CBSE NCERT Class 12 Maths Chapter 1 of the CBSE NCERT Solutions Class 12 Maths Book.** ** They cover all important yet fundamental topics of this chapter, such as relations, types of relations, equivalence classes, functions, algebra of functions, types of functions, and binary operations.

To learn this chapter, you need a holistic approach, and our smart, and well-structured Maths Chapter 1 Relation and Functions** **has been designed taking that into consideration by our subject-matter experts. They not only help you understand the fundamentals of relations and functions but also help you elve deep and obtain an in-depth understanding of all the concepts of this chapter. They clear all your doubts instantly and let you develop a strong conceptual foundation.

With special emphasis on the methodology of the solutions, our NCERT Solutions aims specifically in making you confident and well-equipped to take on even the harder questions from each topic in NCERT CBSE Class 12 Maths Chapter 1. They are easy to understand, drafted in a simple language, and a hundred percent accurate. They are just what you need to excel in your board exams.

## NCERT Class 12 Maths Chapter 1

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions forms the foundation of the higher-order mathematics that is followed in the CBSE NCERT Class 12 Maths Book. Thus a complete understanding of each of the topics of this chapter is imperative. The general overview of the topics covered in this chapter are:

**Relations and its Types**

NCERT CBSE Class 12 Maths Chapter 1 starts with a basic introduction to the definition of relation, according to which two objects or quantities are “related” if there exists a recognizable connection or link between the two objects or quantities; this discussion is followed by the mathematical definition of the relationship between sets of quantities or objects. The discussion continues to the identification and mathematical definitions of different types of relations which primarily are:

- Empty Relation
- Universal Relation
- Reflexive Relation
- Symmetric Relation
- Transitive Relation
- Equivalence Relation

**Functions and its Types**

This section of the NCERT CBSE Class 12 Maths Chapter 1 introduces function as a special type of relational ‘mapping’ where each input has a unique output, followed by the discussion on how a function is a subset of relation and not the other way around. This section builds on the concepts of definitions and criteria for types of functions. The types of functions introduced and discussed here are as follows:

- One-One Function or Injective function.
- Many-one Function
- Onto Function or Surjective function.
- Into Function
- One-One and Onto function or Bijective function.

**Composition of Functions and Invertible Function**

This section deals with the “Composite Function” which refers to the composition of a function, by combining two or more functions in such a manner that the output of one of the functions serves as the input for the next function. This section also introduces you to invertible functions, explaining the criteria for a function to be invertible, followed by discussions on how to compute different compositions of functions and inverses of function provided the necessary criteria are met with.

**Binary Operations**

Introduction to binary operations with definitions and the properties associated with a binary operation are the scopes of study of this section of CBSE NCERT Class 12 Maths Chapter 1. Criteria for the existence of identities of binary operations such as identity for addition ‘+’ and identify for multiplication ‘*’ are also covered in this section. This section also aims to make you well versed with analyzing and giving justifications on whether an operation is binary, and computing operations on such binary operations.

### CBSE NCERT Class 12 Maths Chapter 1: Important Topics

NCERT Class 12 Maths Chapter 1- Relations and Functions comprise of four exercises. Below is a general overview of each of the exercise and its contents:

**EXERCISE 1.1**

Exercise 1.1 of Maths Chapter 1 Relations and Functions has 16 questions. The questions in this exercise build and test your skills. They give you good practice of the different types of relations. The questions require the students to analyze whether the defined relations are reflexive, symmetric and transitive or either of them or all of them, and in the process helps the students get familiar with the fundamental types of relations.

**EXERCISE 1.2**

Exercise 1.2 of NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions has 12 questions that make you accustomed to the different types of functions such as one-one or injective, many-one, onto or surjective, Into, One-One and Onto or bijective. The questions require you to analyze and differentiate amongst the different types of functions. The exercise ends with two multiple-choice questions.

**EXERCISE 1.3**

Exercise 1.3 of this chapter has 14 questions. This exercise builds on the concepts of the composition of functions and invertible functions. Questions 1-3 focus on the composition of functions, followed by questions 4-9 that ask you to analyze and find the inverses of functions provided the criteria are met with. Question 10-12 focuses on the integration of the two concepts of composite functions and invertible functions. The exercise ends with two multiple-choice questions 13-14, both hone your skills with respect to the concepts of the composition of functions and inverse of functions.

**EXERCISE 1.4**

Exercise 1.4 has 13 questions. The exercise starts with question 1, which demands you to analyze and give justification on whether or not certain definitions of operations are binary or not. Question 2 emphasizes the properties of the binary operation. Question 3 asks you to construct an operation table for a given binary operation. Questions 4-13 covers the topics of different properties of binary operations, identities of binary operations, and computation of defined binary operations.

As the concepts of relations, functions and their different types are of paramount importance not only in the domain of mathematics but also other disciplines, Relations and Functions helps to enhance your understanding of these important topics and makes sure to give you a leading edge while you encounter the tougher topics built on these fundamentals.

### Benefits of NCERT Class 12 Maths Chapter –Relations and Functions

There are numerous benefits associated with learning and revising from our NCERT Solutions for Class 12 Maths Chapter 1-Relations and Functions. Some of them have been given below.

- They cover all the topics and sub-topics of the chapter in detail.
- They contained step by step solutions that make complex understanding concepts an easy task.
- Our NCERT Solutions have been drafted in line with the latest CBSE Class 12 Maths Syllabus.
- They have been specifically devised to make learning fun, interesting, engaging and an efficient process.
- They cover all question types that are important from the board exam point of view.
- They help you not only excel in your board exams but also help you in acing various competitive exams.
- They have been drafted using the best methods of solving problem sums to help you learn quickly effectively.
- Our learning shortcuts and effective study strategies give your board exam preparation the right amount of boost and give you a competitive advantage over others.