This is only true if A∩B = Ø, or, mor generally when P(A∩B) = 0.

Why this is so?

Probability theory is an abstract science that draws much of its basics from the experience, meaning that there are two possible arguments:

1. This is very close to observations.
2. A probability function is required axiomatically be additive.

Now, please you should go in greater detail of your specific difficulties.