Set Difference with Superset is Empty Set

Theorem

 * $$S \subseteq T \iff S \setminus T = \varnothing$$

where:
 * $$S \subseteq T$$ denotes that $$S$$ is a subset of $$T$$;
 * $$S \setminus T$$ denotes the set difference between $$S$$ and $$T$$;
 * $$\varnothing$$ denotes the empty set.

Proof
$$ $$ $$ $$ $$

Thus $$S \subseteq T \iff S \setminus T = \varnothing$$.