Cardinality of Set Union

Theorem
Let $S_1$ and $S_2$ be sets.

Then:
 * $\left|{S_1 \cup S_2}\right| = \left|{S_1}\right| + \left|{S_2}\right| - \left|{S_1 \cap S_2}\right|$

Also:

Proof
We have that Cardinality is Additive Function.

From Additive Function is Strongly Additive:
 * $\left\vert{S_1 \cup S_2}\right\vert + \left\vert{S_1 \cap S_2}\right\vert = \left\vert{S_1}\right\vert + \left\vert{S_2}\right\vert$

from which the result follows.