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RD Sharma Solutions for Class 12 Math Chapter 3 - Binary Operations - Free PDF Download

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Last updated date: 16th May 2024
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RD Sharma Class 12 Chapter 3 Free PDF

The keystone of most Algebraic structures, which are studied in Algebra, is Binary Operations. A Binary Operation is a calculation that combines two elements to generate another element. RD Sharma Class 12 Math Chapter 3 on the Binary Operation is an important and most favorable topic in Board Exams and any competitive Exams. The important questions of Binary Operations Class 12 RD Sharma Solutions are created according to the NCERT curriculum and refer to the most important questions asked in the Exams.


These solutions are prepared in a stepwise manner by experts who have vast experience on the subject. The RD Sharma Solutions of Class 12 Maths Chapter 3 important questions will help the students to build strong knowledge about the topic and to excel in their Exams.


Students can download the PDF of Class 12 RD Sharma Solutions for Binary Operations which is freely accessible on the website of Vedantu. When you are stuck in the middle of a problem-solving process, these RD Sharma solutions can help you find a way out with ease and clarity.


While learning the Binary Operations exercises in RD Sharma Solution for Chapter 3 Binary Operations, you must learn a few principles. The following are the principles you must fully comprehend:

  • Understanding the fundamentals of Binary Operations is essential.

  •  Definition and meaning of Binary Operations

  • Binary Operations properties such as Commutativity, Associativity, and Distributivity 

  • Identity element and the inverse of element properties.

  • Multiplication module and composition table.

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Competitive Exams after 12th Science

Important concepts to understand to answer RD Sharma's questions for Class 12 Chapter-3 Binary Operations:

  • Definition and meaning of Binary Operations

  • Number of Binary Operations

  • Binary Operations types

  • Properties such as Commutativity, Associativity, Distributivity

  • Identity element

  • The inverse of an element

  • Composition table

  • Multiplication modulo


You can go ahead with the RD Sharma Solutions for Class 12 Chapter-3 Binary Operations once you have a firm hold on the above topics.


You can use the Binary Operations solution in RD Sharma Solutions Chapter 3 to finish your homework quickly so you can focus on other courses in the CBSE Class 12 curriculum. Please ask any questions you may have in the comments section below.


What are Binary Operations?

A Binary Operation ∗ on set A is a function ∗ : A × A → A. Hence, We denote ∗ (a, b) by a ∗ b.


As Binary means "two" Therefore, A Binary Operation on a set is when two members of the same set are combined to form another element of the same set. Addition, subtraction, multiplication, and division are the most widely known Binary Operations properties.


Consider two elements a and b that form the pair a,bϵ set A. Now, a+b denotes the addition of a and b, while ab denotes the multiplication of a and b. Similarly, we may construct another operator ϕ, such that ϕ performs the Operation a+b−7 i.e,


a ϕ b=a+b−7, then ϕ is a Binary operator of a and b


and a ϕ b is an Example of the Binary Operation.


Note: a ϕ b must belong to set A


3 Main Properties of Binary Operations

1.  Associative property

Let F be a subset of L. A Binary Operation ∗∗ on SS is said to be associative , if (a∗b)∗c=a∗(b∗c),∀a,b,c∈F(a∗b)∗c=a∗(b∗c),∀a,b,c∈F.


2.  Commutative property

Let F be a non-empty set. A Binary Operation ∗∗ on F is said to be commutative, if a∗b=b∗a,∀a,b∈Fa∗b=b∗a,∀a,b∈F.


3.  Distributive property

Let S be a non-empty set. Let ∗2∗2 and ∗∗1∗1  be two different Binary Operations on S.

Then ∗1∗1 is said to be distributive over ∗2∗2 on S if a∗1(b∗2c)=(a∗1b)∗2(a∗1c),∀a,b,c,∈Sa∗1(b∗2c)=(a∗1b∗2(a∗1c),∀a,b,c,∈S.


The Class 12 RD Sharma Solutions are presented simply and exactly based on the students' comprehension abilities. Students who want to do well in the Class 12 Exam can use PDF as a primary study resource to help them prepare for the Exam. Students can acquire RD Sharma Solutions for Class 12 Chapter 3 Binary Operations PDF from Vedantu to gain a better idea of the concepts presented.

FAQs on RD Sharma Solutions for Class 12 Math Chapter 3 - Binary Operations - Free PDF Download

1. What is a binary operation on a set?

An operation whose two domains and the codomain are the same set is a binary operation on a set. Examples include addition, subtraction, and multiplication arithmetic operations.

2. Why do I have to study RD Sharma Solutions of Class 12 Maths Chapter 3?

The solutions to important questions of RD Sharma are created by the Vedantu experts, according to the CBSE syllabus. So these questions are the frequently asked questions in exams. 

3. How important is the binary operation chapter for Class 12 students?

Binary operation is one of the important topics for Class 12 students which teaches the application of relations and functions and also improves students’ logical reasoning skills.

4. Is RD Sharma Solutions Class 12 Math Chapter 3 the most effective Exam study guide?

Yes, RD Sharma Solutions Class 12 Math is the most effective study guide for preparing for the CBSE Class 12 Maths Board Examination. Vedantu's subject experts have compiled these answers, which clearly and precisely outline the fundamental concepts. Referring to RD Sharma Solutions is a requirement for students aiming for a high score in the Class 12 Maths Board Exams.

5. What are the 6 types of properties of Binary Operations?

  • Inverse= a * b = b * a = e, a,b A.a-1. Is invertible if for a * b = b * a = e,a-1 = b . 1

  • Commutative = a * b = b * a 

  • Distributive= a * (b o c ) = ( a * b ) o ( a * c ) o ( b o c ) * a = ( b * a ) o ( c * a )

  • Associative= (a * b) = a * (b*c)

  • Identity= a * e = a = e * a [ e is the identity element ]