In binary operations,

we take two numbers and get one number.

All the numbers are in the same set.

 

For binary operation

* : A × A → A

Binary Operations.jpg

Here,

a, b and a*b all lie in same set A

 

Let's look at some examples


Sum is a binary operation in R

In R (Set of real numbers),

Sum is a binary operation

Let’s take an example

 

For

+ : R × R R

where (a, b) → a + b

Sum as binary operation in R.jpg

For every real number a & b,

a + b is also a real number.

 

Hence, + is a binary operation on R

 


Subtraction is a binary operation in R

In R (Set of real numbers),

Subtraction is a binary operation

Let’s take an example

 

For

– : R × R R

where (a, b) → a – b

  Subtraction as binary operation in R.jpg

For every real number a & b,

a – b is also a real number.

 

Hence, – is a binary operation on R

 


Multiplication is a binary operation in R

In R (Set of real numbers),

Multiplication is a binary operation

Let’s take an example

 

For

× : R × R R

where (a, b) → a × b

  Multiplication as binary operation in R.jpg

For every real number a & b,

a × b is also a real number.

 

Hence,  × is a binary operation on R

 


Division is NOT binary operation in R

In R (Set of real numbers),

Division is not a binary operation

 

For

÷: R × R R

where (a, b) → a ÷ b

 

Here, a & b are real numbers

a ÷ b = a/b

 

Let a = 2 & b = 0

a/b = 2/0 = Not defined

 

Hence, ÷ is not a binary operation on R

  1. Chapter 1 Class 12 Relation and Functions
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 7 years. He provides courses for Mathematics and Science from Class 6 to 12. You can learn personally from here https://www.teachoo.com/premium/maths-and-science-classes/.
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