Commutative Laws of Set Theory

Theorem

Intersection is Commutative

Set intersection is commutative:

$S \cap T = T \cap S$

Union is Associative

Set union is associative:

$A \cup \paren {B \cup C} = \paren {A \cup B} \cup C$

Also defined as

Some sources include in the other identities, for example:

Symmetric Difference is Commutative

Symmetric difference is commutative:

$S \symdif T = T \symdif S$

Also known as

The are also known as the commutative properties (of set theory).

Also see

• Associative Laws of Set Theory
• Distributive Laws of Set Theory

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): algebra of sets: $\text {(ii)}$
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): algebra of sets: $\text {(ii)}$