Author: Ernad Mujakic
Date: 2025-07-20

The commutative property states that the sums and products of values is unaffected by the order those values come in. It allows you to transform mathematical expressions into equivalent forms without altering its value.

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

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

Operations such as subtraction or division are not commutative:

The anti-commutative property refers to specific operations where switching the order of arguments negates the result of the expression.

Subtraction is an anti-commutative operation. Meaning, for any 2 values and :

Some Logical Connectives are commutative, allowing for the rearrangement of variables without changing the truth value of the logical expression.

The commutative property applies to conjunction (AND), for any variables and :

The commutative property applies to disjunction (OR), for any variables and :

In set theory, the commutative property refers to how the Union and Intersection of sets are unaffected by the order of the sets they are applied to.

for any sets , and :

for any sets , and :

The associative property states that the sum or product of any group of values is not affected by how the values are grouped.