NCERT Solutions Class 12 Maths Chapter 1 Exercise 1.3

NCERT Solutions Class 12 Maths Chapter 1 Exercise 1.3: All the 12th class students can prepare for their exams better by studying the NCERT Solutions Class 12 Maths Chapter 1 Exercise 1.3. The solutions are prepared by the subject experts to give your knowledge a boost.

• NCERT Solutions For Class 12 Maths Chapter 1: Relation & Functions

You can download the Free PDF of NCERT Solutions Class 12 Maths Chapter 1 Exercise 1.3. Here you can find the solution to all your problems in a detailed manner and clear your concepts. 

NCERT Solutions Class 12 Maths Chapter 1 Exercise 1.3 PDF

Class 12 Maths NCERT Solutions Chapter 1 Exercise 1.3 pdf

 

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NCERT Solutions Class 12 Maths Chapter 1 Exercise 1.3

 NCERT Solutions Class 12 Maths Chapter 1 consists of the following topics:

1. Introduction 
2. Types of Relations
3. Types of Functions

Introduction

 NCERT Solutions Class 12 Maths Chapter 1 begins by introducing the basic terms. A relation between two sets can be explained as a collection of pairs that consists of one object from each set. For instance, X and Y are objects from set 1 and 2 respectively. When both of them are in the ordered pair, they are said to be related to each other. 

Some of the X and Y relations are shown below to make your understanding of Chapter 1, exercise 1.3 clear:

{(x, y) î X × Y: x is the brother of y},

{(x, y) î X × Y: x is the sister of y},

Types of Relations

NCERT Solutions Class 12 Maths Chapter 1 Exercise 1.3 talks about three types of relations. As mentioned earlier, X is a subset of X x X. It implies that the empty set and X x X are closely related to each other. For example, Relation R, in the set X = {1,2,3,4}, given by R = {(X,Y): X – Y = 10. This will be considered as an empty set because no pair (x,y) satisfies the condition X – Y = 10. Similarly, R = {(X,Y): |x-y| > 0} is the whole set X x X because everything here satisfies the equation. Therefore, both the empty, as well as universal relations can also be known as trivial relations.

Here’s an example for your better understanding. 

Question: The arrangement of all the students of a young boys’ school is represented as X. Show that the relation R in X given by R = {(X, Y): X is the sister of Y}, is an empty relation and R = {(X, Y): the difference between heights of X and Y is under 3 meters}, is a universal relation. 

Solution: Since this is a boys’ school, hence no student can be a female or any students’ sister. It implies that R is an equal set of null showing R is an empty relation. This also shows that the height difference between both the students is under 3 meters, which shows that R = X x X is a universal relation.

Types of Functions 

Before this, we have just understood a bit about the types of relations. Let’s talk about the types of functions now. 

The notion of a function besides some extraordinary capacities such as the personality work, standard capacity, modulus, polynomial capacity, consistent capacity, signum work, etc, have been explained in Class 11. 

Apart from that, we have also covered topics like Addition, Subtraction, Multiplication and Division, related to the concept of functions as it holds a high amount of importance in Maths.

An example is given to make your understanding of the functions clear:

Show: Function f: N. N, given by f(1) = f(2) = 1 and f(x) = x – 1, for every x > 2, is onto but not one-one.

Answer: f is not one-one, as f(1) = f(2) = 1. But in case of f is onto, shown as y N, y 1, now x can be selected as y + 1. such that (y + 1) = y + 1 – 1. For 1 N, f(1) = 1. 

Access Other Exercise NCERT Solutions of Class 12 Maths Relations & Functions

You can download the PDF of NCERT Solutions CBSE Class 12 Maths for Chapter 1 other exercise:

• Exercise 1.1
• Exercise 1.2
• Exercise 1.4
• Exercise 1.5

All the best to the students appearing for the Class 12th board exam. Here is the detailed blog of NCERT Solutions Class 12 Maths Chapter 1 Exercise 1.1. For further queries regarding the Class 12th exam, you can ask in the comment box.

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