Measure is Strongly Additive

Theorem
Let $\left({X, \mathcal A, \mu}\right)$ be a measure space.

Then $\mu$ is strongly additive, that is:
 * $\forall A, B \in \mathcal A: \mu \left({A \cap B}\right) + \mu \left({A \cup B}\right) = \mu \left({A}\right) + \mu \left({B}\right)$