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
