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

Binary Operations - Part 2

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

  Binary Operations - Part 3

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

  Binary Operations - Part 4

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

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.