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

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

In Class XI we already study in brief about relations and functions, range, domain and co-domain with different types of specific real-valued functions and their graphs. In chapter Relations and Functions, we are going to learn about different types of relations and functions, invertible functions, the composition of functions and also binary operations. In this chapter, there are 4 exercises with 55 questions in them and 19 questions in the miscellaneous exercise. The NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions are solved and explained by the subject experts.

## What is the Relation?

Meaning of the term ‘relation’ in mathematics is the same as the meaning of relation in the English language. Relation means two quantities or objects are related if there is a link between two quantities or objects. In other words, we can say that it is a connection between or among things.

Let's understand with an example of NCERT Class 12 Maths Chapter Relations and Functions - let A is the set of students of Class XII of a school and B is the set of students of Class XI of the same school. Then some of the examples of relations from A to B are-

(i) {(a, b) ∈A × B: a is a brother of b},

(ii) {(a, b) ∈A × B: a is a sister of b},

(iii) {(a, b) ∈A × B: age of a is less than the age of b}.

If (a, b) ∈ R, we can say that ‘a’ is related to ‘b’ under the relation ‘R’ and we write as  ‘a R b’. To understand the topic in depth, after every concept, solved examples and exercises are given in CBSE Class 12 Chapter Relations and Functions. In this chapter total 51 solved examples are there, to clear students doubt.

## Topics of NCERT Grade 12 Maths Chapter-1  Relations and Functions

1.1 Introduction

1.2 Types of Relations

1.3 Types of Functions

1.4 Composition of Functions and Invertible Function

1.5 Binary Operations

## Some Examples are-

Question Determine whether each of the following relations are reflexive, symmetric and transitive:

(i) Relation $R$ in the set $A = \{1,2,3 ...,13 ,14\}$ defined as$R = \{(x,y): 3x - y = 0\}$

Solution-

$A = \{1,2,3 ...,13 ,14\}$

$R = \{(x,y): 3x - y = 0\}$ $= \left \{ \left ( 1,3 \right ),\left ( 2,6 \right ),\left ( 3,9 \right ),\left ( 4,12 \right ) \right \}$

Since,  $\left ( 1,1 \right ),\left ( 2,2 \right ),\left ( 3,3 \right ),\left ( 4,4 \right ),\left ( 5,5 \right )\cdot \cdot \cdot \cdot \cdot \cdot \left ( 14,14 \right ) \notin R$ so $R$ is not reflexive.

Since, $\left ( 1,3 \right ) \in R$ but  $\left ( 3,1 \right ) \notin R$ so $R$ is not  symmetric.

Since, $\left ( 1,3 \right ),\left ( 3,9 \right ) \in R$ but $\left ( 1,9 \right ) \notin R$ so $R$ is not  transitive.

Hence, $R$ is neither reflexive nor  symmetric and nor transitive.

(ii) Relation R in the set N of natural numbers defined as
$R = \{(x,y): y = x + 5 \;\textup{and}\;x<4\}$

Solution-

$R = \{(x,y): y = x + 5 \;\textup{and}\;x<4\}$ $= \left \{ \left ( 1,6 \right ),\left ( 2,7 \right ),\left ( 3,8 \right ) \right \}$

Since, $\left ( 1,1 \right ) \notin R$

so $R$ is not  reflexive.

Since, $\left ( 1,6 \right )\in R$ but $\left ( 6,1 \right )\notin R$

so $R$ is not symmetric.

Since,there is no pair in  $R$ such that $\left ( x,y \right ),\left ( y,x \right )\in R$ so this is not transitive.

Hence, $R$ is neither reflexive nor symmetric and
nor transitive.

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions- Solved Exercise Questions

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.1

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.2

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.3

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Miscellaneous

## NCERT Solutions for class 12- Maths

 Chapter 2 Inverse Trigonometric Functions Chapter 3 Matrices Chapter 4 Determinants Chapter 5 Continuity and Differentiability Chapter 6 Application of Derivatives Chapter 7 Integrals Chapter 8 Application of Integrals Chapter 9 Differential Equations Chapter 10 Vector Algebra Chapter 11 Three Dimensional Geometry Chapter 12 Linear Programming Chapter 13 Probability