Union is Associative

Theorem
Set union is associative:


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

Proof
Therefore:
 * $x \in A \cup \paren {B \cup C}$ $x \in \paren {A \cup B} \cup C$

Thus it has been shown that:
 * $A \cup \paren {B \cup C} = \paren {A \cup B} \cup C$

Also see

 * Intersection is Associative
 * Set Difference is not Associative
 * Symmetric Difference is Associative