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)

Associative Binary Operations.jpg

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)

Associative Binary Operations Multiplication.jpg

 

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)

Associative Binary Operations Subtraction.jpg

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)

Associative Binary Operations Division.jpg

Since (a * b) * c ≠ a * (b * c)

÷ is not an associative binary operation

  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 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.