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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

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

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

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

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
**