##  [Associative Law](/index.php/associative-law) 

  ##  [Associative Law](https://mathlogic.quantumdictionary.io/associative-law-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/index.php/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The law that the way operands are grouped in repeated application of a binary operator does not affect the result; formally, for operator ⊗ and operands A, B, C: (A ⊗ B) ⊗ C = A ⊗ (B ⊗ C) (example: (A ∧ B) ∧ C = A ∧ (B ∧ C)).

 

 

 

 

 





 

 



 ##  [Associative Law](https://puremath.quantumdictionary.io/associative-law-1) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/index.php/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A binary operation * on a set satisfies the associative law if for all a,b,c one has (a*b)*c = a*(b*c); the placement of parentheses does not affect the result of successive applications of the operation.

 

 

 

 

 





 

 



 ##  [Associative Law](https://algebra.quantumdictionary.io/associative-law-2) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/index.php/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The algebraic property of a binary operation whereby the grouping (parenthesization) of operands does not change the result: for all a, b, c in the domain, (a·b)·c = a·(b·c).