For binary operation

* : A × A → A

If (a * b) * c = a * (b * c)

Then it is

associative binary operation

##
**
Addition
**

+ :
**
R
**
×
**
R
**
→
**
R
**

* is associative if

(a * b) * c = a * (b * c)

Since (a * b) * c = a * (b * c) ∀ a, b, c ∈
**
R
**

+ is an
**
associative
**
binary operation

##
**
Multiplication
**

× :
**
R
**
×
**
R
**
→
**
R
**

* is associative if

(a * b) * c = a * (b * c)

Since (a * b) * c = a * (b * c) ∀ a, b, c ∈
**
R
**

× is an
**
associative
**
binary operation

##
**
Subtraction
**

– :
**
R
**
×
**
R
**
→
**
R
**

* is associative if

(a * b) * c = a * (b * c)

Since (a * b) * c ≠ a * (b * c) ∀ a, b, c ∈
**
R
**

– is
**
not an associative
**
binary operation

##
**
Division
**

÷ :
**
R
**
×
**
R
**
→
**
R
**

* is associative if

(a * b) * c = a * (b * c)

Since (a * b) * c ≠ a * (b * c)

÷ is
**
not an associative
**
binary operation

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