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

• 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.