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# NCERT Solutions for Class 11 Maths Chapter 2 – Relations and Functions

NCERT Solutions for Class 11 Maths Chapter 2 are created by our maths subject experts for instant doubt solving. This chapter on Relations and Functions is directly related to the earlier chapter on Sets. There are 4 exercises in the chapter with a total of 41 questions. We have prepared exercise-wise solutions for the chapter so that you can find the right answers to your doubts easily.

NCERT Class 11 Maths Chapter 2 discusses topics like finding the value of elements in a given set, finding the number of elements in the two given sets, solving triple ordered sets, finding remaining elements of a given set using the cartesian product method. Preparing NCERT solutions will help you revise all these topics once again after school and will help you prepare the chapter well for your exams.

All our NCERT solutions for this chapter are as per the latest Class 11 CBSE Maths syllabus. So you can easily rely on our explanations and problem-solving methodology. Our solutions will make it easier for you to understand the tough concepts of the chapter. You must know that this chapter is important for other chapters as well such as Limits and Derivatives, Continuity and Differentiability, Application of Derivatives, Integrals, Application of Integrals to Differential Equations etc. Let’s jump into the summary of NCERT Class 11 Maths Chapter 2.

## Important Topics for NCERT Solution for Class 11 Mathematics Chapter 2: Relations and Functions

Relations

In CBSE, NCERT Solutions for Class 11 Maths Chapter 2, you will learn how to make links between the elements from the two sets. Then, it introduces relations between the two elements in the pair. Let us understand by taking examples of real-life relations such as brother-sister, father-son, teacher-student etc. Similarly, in maths, if we say that 2 is smaller than 7, it is a relation. Again, 5 is greater than 3 is also a relation.

One thing to be noted is that relation is always in pairs. The chapter also talks about special relations called functions.

Cartesian Product

To understand Functions, we first have to understand the term Cartesian Product of Sets. Let us see this with the help of an example. Suppose there are two non-empty sets- A = {1, 2, 3}, and B = {4, 5, 6}, the Cartesian Product of Sets A and B here will be in the following way:

1. We will multiply the first element of set A that is 1 to the other elements of the set B that are 4, 5, and 6;
2. Similarly, we will multiply the second element of A that is 2 with the rest of the sets of B that are 4, 5, and 6;
3. On multiplying, we will get ordered pairs such as {(1,4), (1,5), (1,6), (2,4), (2,5), (2,6), (3,4), (3,5), (3,6)} etc.

The above pairs are called Ordered Pair because they are arranged in a sequence in such a way that the first element of each pair will belong to A, which is the first set and the second element will belong to set B, which is the second set. In the same way, if we are required to cross the B set with A set, the elements of set B will come first and make Ordered Pairs in the same way.

In NCERT the same process is being described with the help of graphic representations. Thus, Cartesian Product of sets can be defined as the given two non-empty sets A and B, the Cartesian product of set A and B i.e., A * B is the set of the ordered pairs of elements from A and B.

Relations

Now, we will talk about relations. A Relation R from a non-empty set A to a non-empty set B is a subset of the Cartesian product set A * B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A * B. The set of all first elements in a relation R, is called the domain of the relation R, and the set of all second elements called images, is called the range of R.

A function is also a kind of relation, which describes that there should be only one output for each input. In other words, we can also say that it is a special kind of relation which follows a rule i.e. every x-value associated with only one y-value. In addition to this, the chapter also describes the types of relations and functions in detail.

Some Important Definitions:

1. If either of the sets is null then, the product will be a null set only with no ordered pairs;
2. If A and B is an infinite set, then the Cartesian Product of the two will be an infinite set;
3. In the case of two equal Ordered Pairs, the first element will be equal to the first element, and the second element will be equal to the second element;
4. The total number elements in an Ordered Pair will be the multiplication of the ordered set of the two sets;
5. An Ordered Triplet is basically about the multiplication of three sets – A, B and C;
6. A relation may be represented either by the roster form or by the set builder form, or by an arrow diagram which is a visual representation of a relation;
7. All functions are relations, but not all relations are functions.

### Exercise- wise discussion on NCERT Solutions Class 11 Mathematics Chapter 2

1. Exercise 2.1 consists of 10 questions based on the concepts of sets.
2. Exercise 2.2 has 12 questions that will test your understanding regarding chapter Relations and Functions.
3. Exercise 2.3 has 5 questions related to the domains as well as finding the range.
4. The last exercise is the miscellaneous exercise that will examine your understanding regarding the overall concepts of the chapter.
5. By solving these exercises, you will get confidence to appear in the examination.

### About NCERT Solution for Class 11 Maths Chapter 2 by Instasolv

1. The NCERT solutions for class 11 maths chapter 2 provided by Instasolv will help you to understand the concepts related to Relation and Function better
2. We have created the solutions in an easy to understand the language
3. The questions are described for you in such a way that you can correlate the entire lesson and comprehend it yourself
4. We don’t provide any important set of questions, rather we provide a solution for each and every topic so that you can grasp everything at the very first instance.
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