# RD Sharma Class 11 Chapter 2 Solutions (Relations)

RD Sharma Solutions for Class 11 Maths Chapter 2 ‘Relations’ are crafted in a simplified manner so that you can learn basic concepts of relations easily. In this chapter, we have come up with a beginner’s guide which will make you understand the complexities of relationships and gain in-depth knowledge for the betterment of their future. RD Sharma Class 11 Maths Solutions will surely help you achieve higher numbers in the CBSE exams as well as boost the confidence for attempting complex problems of JEE and NEET.

In chapter 2, you will study Relations also known as the cartesian product of sets. Starting from the basic concept of relations to solving exercises you may find relations quite difficult if you are not familiar with the basics. The topics you usually go through are the cartesian product of sets, equality of two ordered pairs, finding relations and finding range & domain. RD Sharma Class 11 Maths Chapter 2 ‘Relations’ has 3 exercises with 69 questions.

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## Topics covered in RD Sharma Solutions for Class 11 Chapter 2 – Relations

To understand relation you need to have a basic understanding of sets first. A relation is fundamentally about two sets between two sets.

For example, if you have two sets namely Set Y and Set Z the relation defined by R from set Y to Set Z is yRz. Here y and z are the crucial elements of Set Y and Set Z. Here the relation between the set Y and Set Z is actually the subset of the cartesian product of Y and Z.

A relation can also be defined as the collection of ordered pairs (y,z) where a is the elements of set Y and Z belong to the elements of Set Z with a relation Y to Z i.e yRz but not Z to Y in any case.

**Ordered pairs**

If you have two sets namely Set Y and Set Z then (y,z) is known as an ordered pair. Then for the Set Y and Set Z one sets are known as primary sets because of first elements.

On the other hand, the second one is treated as a secondary set and features secondary elements. Ordered pairs are primarily used for cartesian products and relations. The two ordered pairs are equal if and only y1=y2 & z1=z2

**Cartesian Product of two sets**

The cartesian product of two sets is defined as the set of all the probable ordered pairs in between two sets adhering to a sequence. It is described as Y X Z or Z X Y where both Y X Z Z X Y are completely different.

**Domain & range of Any relations **

In a relation R from Set Y to Set Z, the set of primary elements of an ordered pair is known as the Domain of a relation. On the other hand, the set of secondary elements of the ordered pairs R is known as the range.

**The inverse of a Relation**

The inverse of a relationship is simply known as the opposite any relation and it is defined as **R ^{-1}**

It shows if R is the relation from X to Y then the inverse of the relation will be Y to X and it is defined as **R ^{-1 }**= {(y,x) | (x,y) ∈R}

**Types of Relations**

There are mainly four types of relation along with different properties. They are as follows

- Identity relation
- Symmetric relation
- Reflexive relation
- Transitive relation

## Exercises of RD Sharma Solutions for Class 11 Chapter 2 – Relations

- RD Sharma Solutions for Chapter 2 Relations exercises covers mainly algebra of real functions, a cartesian product of sets, Equality of ordered pairs as the primary components of relation.
- Chapter 2 relations features three exercises. Exercise 2.1 houses a total of 14 questions, exercise 2.2 houses 7 questions and 2.3 has a total of 9 questions.
- The first exercise is primarily about the introduction of relations and cartesian product of sets whereas the second exercise describes the domain and range of the relation R, visual representation of relations.
- The third exercise is based on the types of relations and codomain, domain and range of a relation.

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