Union is Associative

Theorem
Set union is associative:


 * $A \cup \left({B \cup C}\right) = \left({A \cup B}\right) \cup C$

Proof
Therefore, $x \in A \cup \left({B \cup C}\right)$ iff $x \in \left({A \cup B}\right) \cup C$.

Thus it has been shown that:
 * $A \cup \left({B \cup C}\right) = \left({A \cup B}\right) \cup C$

Also see

 * Intersection is Associative
 * Set Difference is Not Associative
 * Symmetric Difference is Associative