If we have $a$ ways of doing one thing and $b$ ways of doing another thing but we cannot do both at the same time, then there are $a+b$ ways to choose to do one thing.
Set theoretically, the sum of the sizes of a finite collection of pairwise disjoint sets is the size of the union of the sets. That is, \(\vert S_1\vert + \vert S_2\vert + \cdots + \vert S_n\vert = \vert S_1\cup S_2\cup\cdots\cup S_n\vert .\)
Wikidata ID: Q2360148