Set Difference of Larger Set with Smaller is Not Empty

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Theorem

Let $S$ and $T$ be finite sets.

Let $\card S > \card T$.


Then:

$S \setminus T \ne \O$


Proof

From Cardinality of Subset of Finite Set:

$S \not \subseteq T$

From the contrapositive statement of Set Difference with Superset is Empty Set:

$S \setminus T \ne \O$.

$\blacksquare$