Union with Empty Set

Theorem
The union of any set with the empty set is the set itself:


 * $$S \cup \varnothing = S$$

Proof 1
$$ $$ $$ $$ $$

Proof 2
From Empty Set Subset of All, $$\varnothing \subseteq S$$.

From Union with Superset is Superset‎ it follows that $$S \cup \varnothing = S$$.