# RD Sharma Class 12 Chapter 3 Solutions (Binary Operations)

RD Sharma Solutions for Class 12 Chapter 3 – Binary Operations will help you perform well in your CBSE board exams. RD Sharma reference book is known to be the most informative and challenging practice books for class 12. This book is proven to be the best as it helps in mastering the entire maths syllabus in an organized manner.

Before you start practising the questions of this chapter of RD Sharma Solutions, you must solve the questions of chapters 1 and 2 of the book that is, relations and functions. You must also know sets and their properties. Chapter 3 of RD Sharma Class 12 Maths book contains several topics like binary operations, the closure property, properties of binary operations, associative law, distributive law and commutative law. This chapter has 7 exercises with a total of 123 questions.

At Instasolv, you will find stepwise RD Sharma solutions for the chapter of binary operations. We have also provided proper reasoning with each question so that you can revise the formulae and the properties side by side. We ensure that all the solutions are as per the latest CBSE syllabus and exam pattern.

## Important Topics of RD Sharma Solutions for Class 12 Chapter 3 – Binary Operations

**Binary Operations **

Like you get a number when two numbers are either added or subtracted, multiplied or divided, similarly, binary operation refers to the two elements of a set. The result of the two is also in the same set. Binary operation refers to the calculation that combines the two elements of the set (known as operands) so as to produce another element for the same set.

**Properties of a Binary Operation**

- An operation on a non-empty set A contains closure property, if a A, b B, a * b A.
- Additions, Multiplication and Subtraction are also the binary operations on each of the sets of Natural numbers (N), Integer (Z), Rational numbers (Q), Real Numbers (R), Complex numbers (C).
- The addition, multiplication, and subtraction that takes place on the set of all irrational numbers is not a binary operation.
- Division is not a binary operation on a set of natural numbers, integers, rational numbers, real numbers, and complex numbers.

**Types of Binary Operations**

**Commutative = a * b = b * a**- Associative= (a * b) = a * (b*c)
- Distributive= a * (b o c ) = ( a * b ) o ( a * c ) o ( b o c ) * a = ( b * a ) o ( c * a )
- Identity= a * e = a = e * a [ e is the identity element ]
- Inverse= a * b = b * a = e, a,b A.a-1. Is invertible if for a * b = b * a = e,a-1 = b . 1

## Exercise Discussion of RD Sharma Solutions for Chapter 3 – Binary Operations

- Exercise 3.1 of RD Sharma Class 12 Solutions Maths Chapter 3 has more than 20 questions in which you have to determine if the given operations can be called binary operations or not.
- Exercise 3.2 has around 24 questions based on the commutative, associative and distributive properties of binary operations.
- In Exercise 3.3, there are questions related to finding the identity element of the binary operations.
- Exercise 3.4 is very important as it contains the main questions related to the chapter. You have to prove some theorems, find identity and invertible elements and determine if the operations are binary or not.
- In exercise 3.5, you have to construct the composition table, find the inverse elements, and create binary operations.
- Then, there are two exercises of very short answer type questions and multiple-choice questions respectively. These exercises include questions based on all the fundamental elements of the chapter.

## Benefits of RD Sharma Solutions for Class 12 Chapter 3 – Binary Operations by Instasolv

Instasolv provides you with the best RD Sharma Class 12 Maths Solutions that are designed by our professional experts. We provide you with accurate and complete solutions for each question that is mentioned in the RD Sharma Class 12 Maths Chapter 3.You can easily access all the chapter-wise and exercise-wise questions and answers.

The Instasolv team has made the solutions in a step-by-step approach, for your better understanding of the chapter. RD Sharma Solutions for Chapter 3 by Instasolv will help you in preparing for school level and graduate-level exams like KVPY, IMO, CAT, IIT JEE, etc. All these solutions will help you in having a good grip on the basic mathematical concepts of binary operations.