# RS Aggarwal Class 11 Chapter 2 Solutions (Relations)

RS Aggarwal Solutions for Class 11 Chapter 2 ‘Relations’ will help you learn topics like how we create a relation between two sets by linking up the pairs of objects from both the sets. You will basically get to know how to make relations between the sets. Chapter 2 Relations of RS Aggarwal Class 11 Maths Solutions book consists of 5 exercises and a total of 63 questions.

The chapter consists of important topics like domain and range of a relation, inverse of a relation, relation in a set, identity relation, universal relation in a set and void relation in a set. RS Aggarwal has many questions containing all these topics and clearing all the important points of the topics for CBSE exam preparation.

Relations Chapter 2 are prepared by our best math experts. Every solution has a detailed explanation which makes it easy for students to understand the topics and get a detailed understanding of the chapter. These solutions will bring clarity to you and you will be able to handle all kinds of questions related to the topic ‘Relations; in your exams. We have solved every question in a stepwise manner and have provided clear explanations for your reference.

## Important Topics of RS Aggarwal Solutions for Class 11 Chapter 2

When we define Relations, we can say that it is a relationship between sets of values. The relation is between the x and y values of the pairs which are ordered. In this RS Aggarwal Solutions for Class 11, Relations and its domain and range are explained with the help of different types of questions and these questions clear the basis of the chapter.

**Cartesian Product of Sets**

Under this category, you will get to know how to find the product of cartesian products in different questions. Also, you will know what is an ordered pair when the cartesian product is equal, or how to find the cartesian product of three different sets. Other findings include finding the number of elements in any cartesian products etc.

Suppose there are two empty notes sets A and B. So, the cartesian product of A and Bis the set of all ordered pairs of elements from A and B.

A x B = {(a,b): a ∈ A, b ∈ B}

Let A = {a1, a2, a3, a4} and B = {b1, b2}

Then, the cartesian product A and B will be

A x B ={a1b1, a2b1, a3b1, a4b1, a1b2, a2b2, a3b2, a4b2}

Example: let us say, X = {abc}, Y = {123}

Therefore, X x Y = {a1, a2, a3, b1, b2, b3, c1, c2, c3}. This set has 8 ordered pairs. You can also represent it as in a tabular form.

In the chapter, you will know how to use this set in different questions.

**Note: **two ordered pairs X and Y are equal, if and only if the corresponding first element and second elements are equal.

**Relations**

**Definition: **A relation R is the subset of the cartesian product of X x Y, where X and Y are two non-empty elements. It’s derived by stating the relationship between the first element and the second element of the ordered pair of X x Y.

## Important points of RS Aggarwal Class 11 Chapter 2

- Relations are of 3 types – Empty relation, Universal relation, Trivial relations.
- If A and B be two non-empty finite sets, containing m and n elements respectively, then the total number of relations from A to B is 2mn
- The image of an element x under a relation R is given by y, where (x, y) ∈ R
- A Relation R in a set A is said to be an equivalence relation if R is reflexive, symmetric and transitive
- Two ways of representing a relation are the Roster method and Set builder method.

## Exercise-Wise Discussion Of RS Aggarwal Chapter 2 Relations

This chapter has around 5 exercises with approximately 80 questions that cover different topics of the chapter. The exercises are 2A, 2B, 2C, 2D, 2E.

**Exercise 2A**

In this exercise, you will have to find the values of a and b if the ordered pairs are equal, using the cartesian product of sets, etc. Also, you will then have to prove the situations asked in the question. There are 14 questions in this exercise.

**Exercise 2B**

In this set of the exercise, you will have to prove the situations like;

A x (B ∪ C) = (A x B) ∪ (A x C) etc. There are 9 questions in this exercise.

**Exercise 2C**

This exercise set has 14 questions on finding the relation between two non-empty sets like A and B. Also, in different questions, you will be asked to find the domain and range of any relation.

**Exercise 2D**

In this exercise, you will have to test your skill based on binary relations, finding domain and range of a particular relation set, expressing the relation as an ordered set of pair, showing a relationship as an equivalence relation, etc. It has 14 questions.

**Exercise 2E**

In this exercise, you will have to find n(AxB) in different situations, proving different other questions, finding the possible subsets, writing the relation in roster form, or finding the domain and range of the given relation set. There are 12 questions in this exercise.

## RS Aggarwal Class 11 Maths Solutions for Chapter 2 by Instasolv

RS Aggarwal is one of the famous reference books for the students of class 11. Chapter 2 of the book is a continuation of chapter 1. Both the chapters are important from exam point of view and our RS Aggarwal solutions will prepare you for the same. You can refer to our solutions for exam preparation of JEE and NEET as well along with CBSE exams. We thoroughly understand that the course content is getting difficult and you might be unable to find solutions to the questions. But now, there is nothing to worry about as the Instasolv team works together to provide you with the best solutions timely. You will be able to get access to every question no matter wherever you are.