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# RD Sharma Class 12 Solutions Chapter 3 - Binary Operations (Ex 3.2) Exercise 3.2 Last updated date: 23rd Nov 2023
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## RD Sharma Class 12 Solutions Chapter 3 - Binary Operations (Ex 3.2) Exercise 3.2 - Free PDF

Free PDF download of RD Sharma Class 12 Solutions Chapter 3 - Binary Operations Exercise 3.2 solved by Expert Mathematics Teachers on Vedantu.com. All Chapter 3 - Binary Operations Ex 3.2 Questions with Solutions for RD Sharma Class 12 Math to help you to revise the complete syllabus and score more marks. Register for online coaching for IIT JEE (Mains & Advanced) and other engineering entrance Exams.

The Solutions for Chapter 3 – Binary Operations in RD Sharma Class 12 include all of the questions from the textbooks prepared by Vedantu’s Mathematics expert teachers. Download our free PDF of Chapter 3 – Binary Operations RD Sharma Solutions for Class 12 to help you score higher on your board Exams and competitive tests.

The solutions for Class 12 Math Chapter 3 are provided here to assist students in discovering simple ways to solve various problems. The solutions we provide are intended to help students understand the topic of Binary Operations in greater depth and learn how to solve Math problems relating to it. These solutions can assist students in improving their Math fluency and revising the entire curriculum. Students can view the RD Sharma solutions for Class 12 Chapter 3 online on the website by clicking the links provided below, or they can save it for later use.

## Binary Operation

The basic Mathematical Operations of addition, subtraction, division, and multiplication can be performed on two operands. In case we have to add three numbers, we add two and then add the third to the result of the first two. As a result, the basic Mathematical Operations are known as Binary Operations because they are performed on two numbers (the word Binary means two). In this section, we will look at Binary Operations on a set.

### What exactly is Binary Operation?

As X, we consider the set of numbers on which the Binary Operations are performed. The Operations (addition, subtraction, division, multiplication, and so on) can be generalized as a Binary Operation on two elements (say, a and b) from set X. The Operation on a and b yields another element from the same set X.

As a result, the Binary Operation can be defined as an Operation * performed on a set A. The function is denoted by *: A * A → A. As a result, the Operation * on operands a and b is denoted by a * b.

### Binary Operation Types

Binary Operations are Classified into four types:

• Binary Subtraction

• Binary Multiplication

• Binary Division

The complete details for each Operation can be found in the linked lessons, and an Example question is provided below to help with comprehension.

### Examples of Binary Operations

Let us demonstrate that addition is a Binary Operation on real ® and natural (N) numbers (N). So, if we add two natural numbers, a and b, the result will also be a natural number.

The same is true for real numbers. As a result,

+ : R x R → R can be (a, b) → a + b

+ : N x N → N can be (a, b) → a + b

Let’s demonstrate that multiplication is a Binary Operation on real ® and natural (N) numbers (N). So, if we multiply two natural numbers, a and b, the result will be a natural number as well. The same is true for real numbers. As a result,

x: R x R → R is given by (a, b) → a x b

x: N x N → N is given by (a, b) → a x b

Let us demonstrate that subtraction is a real-number Binary Operation ®. So, if we subtract two real-number operands, a and b, the result will also be a real number. The same cannot be said in the case of natural numbers. This is because when we take two natural numbers, 3 and 4, as a and b, then 3 – 4 = -1, that cannot be termed a natural number. Therefore,

–: R x R → R can be (a, b)→ a – b

Similarly, division cannot be done in terms of the real numbers. The reason being / : R x R → R  can be  (a, b)→ aa/b. If we set b to zero, a/b is not defined.

## FAQs on RD Sharma Class 12 Solutions Chapter 3 - Binary Operations (Ex 3.2) Exercise 3.2

1. Where can I get the RD Sharma Class 12 Math Chapter 3 Solutions?

The RD Sharma Solutions for Class 12 Math Chapter 3 are available on the Vedantu website in both online and offline formats. The RD Sharma Class 12 Solutions are available in PDF, which you can easily download free.Vedantu subject experts prepared the RD Sharma Solutions in accordance with the most recent CBSE guidelines and marking schemes. Log in to the Vedantu website or mobile app with the registered mobile number and start your learning with fun.

2. Where can students find the most up-to-date RD Sharma Class 12 Solutions Chapter 3?

Students can get the most up-to-date RD Sharma Class 12 Solutions from the Vedantu website. RD Sharma textbooks are the best study materials because they provide a wide range of practice questions for both students and teachers. RD Sharma Solutions are meticulously prepared to assist students in easily understanding concepts and racing board Examinations. The solutions of RD Sharma for Class 12 Math Chapter 3 are provided here to assist students in discovering simple ways to solve various problems. The solutions we provide are intended to help students understand the topic of Binary Operations in greater depth and learn how to solve Math problems relating to it.

3. Is RD Sharma Solutions Class 12 Math Chapter 3 the best Exam prep material?

Yes, RD Sharma Solutions Class 12 Math is the best study material for preparing for the CBSE board Exams. Vedantu subject experts curate these solutions, which clearly and precisely outline the main concepts. Referring to RD Sharma Solutions is a must for students aspiring to achieve an excellent score in the Class 12 Math board Exam. These solutions can assist students in improving their Math fluency and revising the entire curriculum. Students can view the RD Sharma solutions for Class 12 Chapter 3 online on the website by clicking the links provided below, or they can save it for later use.

4. What topics are covered in Chapter 3 of RD Sharma Solutions for Class 12 Math? Mention the benefits of using RD Sharma Solutions for Class 12 Math Chapter 3?

The following concepts are covered in RD Sharma Solutions for Class 12 Math Chapter 3:

The definition and significance of Binary Operations

• Count of Binary Operations

• Binary Operation types

• Commutativity

• Associativity

• Distributivity

• Element of individuality

• The element's inverse

The R D Sharma Solutions developed by experts at BYJU'S offers numerous advantages to students preparing for their final Exam. Each concept provides a thorough explanation and assists students in achieving high grades. The solutions strictly adhere to the current CBSE 2021-22 syllabus. These solutions will assist students in preparing for other competitive Exams in addition to Class 12 board Exams.

5. How can I do well in Class 12 Math?

The only way to do well in Class 9 Math is to practise. Complete all of the Chapter exercises. This will enhance your problem-solving abilities as well as your speed and efficiency. Important formulas, definitions, and equations can be written down in a notebook and reviewed regularly. Solve previous year's sample papers and question papers within a time limit. This will familiarize you with the paper pattern and question type, as well as help you improve your time management skills. Revise regularly to ensure that you retain everything you've learned for a longer period following.