Cardinality of Set Union

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

Then:
 * $\card {S_1 \cup S_2} = \card {S_1} + \card {S_2} - \card {S_1 \cap S_2}$

Also:

Proof
We have that Cardinality is Additive Function.

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

from which the result follows.