# RD Sharma Solutions Class 12 Maths Chapter 3 – Binary Operations (Updated for 2021-22)

RD Sharma Solutions Class 12 Maths Chapter 3 – Binary Operations: Here are the RD Sharma Solutions for Class 12 Chapter 3 – Binary Operations solutions in PDF format. Students who are facing difficulty in solving the exercise wise problems of Chapter 3 can download the exercise-wise solutions PDF of RD Sharma Solutions.
The RD Sharma Solutions for Class 12 are presented in a simple and concise manner, taking into account the students’ understanding abilities. Students who want to do well on the Class 12 exam should use PDF as a primary study material. Students can get RD Sharma Solutions for Class 12 Chapter 3 Binary Operations PDF from here to acquire a better understanding of the concepts covered here.

RD Sharma Solutions Class 12 Maths Chapter 3

RD Sharma Solutions Class 12 Maths Chapter 3 PDF is available for free download. The RD Sharma solutions assist you to find a way out when you are stuck somewhere in the problem-solving process.

## Detailed Exercise-wise RD Sharma Solutions Class 12 Maths Chapter 3 – Binary Operations

You need to understand a few concepts while studying binary operations exercises of RD Sharma Solution Chapter 3. The concepts you need to understand thoroughly are:

• Understanding the basics of Binary operations
• The definition and meaning of Binary operations
• Number of binary operations, such as Commutativity, Associativity, and Distributivity
• Concepts of an identity element and the inverse of an element
• Composition table and multiplication module

### Brief descriptions of the Questions in Class 12 Maths Chapter 3

Exercise 3.1 Question 1: You need to determine whether the operations given in the question define a binary operation on the set.

Exercise 3.1 Question 2: You need to determine whether * mentioned in the question gives binary operation. You need to justify in the event the * is not a binary operation.

Exercise 3.1 Question 3: In this question, you will be given * to be considered as a binary operation on the set I of integers defined in the question, and you are required to answer the question by determining the value of 3*4.

Exercise 3.1 Question 4: You need to determine whether * given the set as mentioned in the question a binary operation and you need to justify your answer.

Exercise 3.1 Question 5: S is defined in the question, and you need to determine the total number of binary operations on S.

Exercise 3.2 Question 1: In this question, you are given * to be considered as a binary operation on N defined, and you are required to find 2*4, 3*5, 1*6 and check the Commutativity and associativity of the binary operation * on N.

Exercise 3.2 Question 2: In this question, out of a couple of binary operations given and you need to determine associative one and commutative one out of the given options.

Exercise 3.2 Question 3: You are given a set A which contains more than one element. You are instructed in the question to consider * as the binary operation on A defined, you need to find out if * is commutative or associative.

Exercise 3.2 Question 4: You need to check the Commutativity and associativity of binary operations given in the question.

Exercise 3.2 Question 5: o is defined as binary operation in the question on the set Q which consists of rational numbers but 1. You need to explain the process of the binary operation o is commutative on Q.

Exercise 3.2 Question 6: The binary operation * on Z is defined in the question and your job would be to establish that that binary operation * is not commutative.

Exercise 3.2 Question 7: Z is a set of integers that is given in the question. The binary operation * is defined. You need to show that the binary operation * is not associative on Z.

Exercise 3.3 Question 1: In this section, you will practice exercises and solutions on how to find out the identity element. Your job as part of the solution is to identify the identity element in the set.

Exercise 3.3 Question 2: In this exercise, your job is to identify the identity element in the set w.r.t * as defined.

Exercise 3.4 Question 1: The binary operation * in this question is on z defined. You need to show * as commutative and associative, find identity element in Z, and invertible element in Z.

Exercise 3.4 Question 2: The binary operation * is on Q0 asset. Your job is to establish the binary operation is commutative and associative. Additionally, you need to find its identity element exists.

Exercise 3.4 Question 3: The binary operation * is defined and you need to show that the binary operation is commutative as well as associative on Q. Additionally, you need to find the identity element in Q to show that every element on Q is invertible. In the same question, you will determine the inverse of an arbitrary element.

Exercise 3.4 Question 4: You need to show the binary operation O defined on A is commutative and associative on A.  Need to find out identity element and invertible element in A.

Exercise 3.5 Question 1: You are required to construct a composition table for x4 on set S.

Exercise 3.4 Question 2: In this question also, you practice how to construct the composition Table defined in the question.

Exercise 3.4 Question 3: You need to construct a composition Table for x6 on Set S defined in the question.

Exercise 3.4 Question 4: You need to construct a composition Table for x5 on Set Z5 defined in the question.

Exercise 3.4 Question 5: You need to construct a composition Table for x10 on Set S defined in the question and also to find the inverse of 3.

## Important Concepts Under Class 12 Maths Chapter 3

Concepts that are important to know to be able to solve questions of RD Sharma Solutions of Chapter 3 class 12 maths include:

• Definition and meaning of binary operations
• Number of binary operations
• Types of binary operations
• Commutativity
• Associativity
• Distributivity
• Identity element
• The inverse of an element
• Composition table
• Multiplication modulo

Once you have clear concepts on the above topics, you can go ahead and refer to the RD Sharma Solutions of Chapter 3 for Binary operation class 12 maths.

You can leverage the solution of Binary Operations in RD Sharma Solutions Chapter 3 to complete your homework fast so you can concentrate on other subjects of CBSE Class 12 curriculums. If you have any queries, feel free to ask us in the comment section below.

## FAQs on RD Sharma Solutions Class 12 Maths Chapter 3

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