Author: Ernad Mujakic
Date: 2025-07-19

The associative property states that the sum or product of any group of values is not affected by how the values are grouped. It allows you to transform mathematical expressions into equivalent forms without altering its value.

The associative property applies to addition. For any numbers , and :

The associative property applies to multiplication. For any numbers , and :

The associative property applies to matrix multiplication as well. For matrices , , and with compatible dimensions:

Operations such as subtraction or division are not associative:

In Propositional Logic, associativity is a rule of replacement that applies to some Logical Connectives, allowing for the rearrangement of grouping symbols without changing the truth value of the logical expression.

Associativity applies to conjunction (AND), for any variables , , and :

Associativity applies to disjunction (OR), for any variables , , and :

In set theory, the associative property refers to how the Union and Intersection of sets can be grouped without altering the outcome of the expression.

for any sets , , and :

for any sets , , and :

The commutative property states of values does not effect their sum or product.

Note that the commutative property does not apply to matrix multiplication.