Tests for Finite Set Equality

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

Let $S \subseteq T$.


 * $(a):\quad \card S = \card T$
 * $(b):\quad \card {T \setminus S} = 0$
 * $(c):\quad T \setminus S = \O$
 * $(d):\quad T = S$

Proof
We have: