Addition principle
= Addition principle
{title2=$|A\sqcup B|=|A|+|B|$}
{wiki}
= Rule of sum
{synonym}
The <rule of sum> counts alternatives in disjoint finite <sets> by adding their sizes. For a <disjoint union> $A\sqcup B$, each element belongs to exactly one alternative, so $|A\sqcup B|=|A|+|B|$. Overlapping alternatives require accounting for repeated elements, as in the <inclusion-exclusion principle>. The groups indexed by first-return position in the <Catalan recurrence> are disjoint alternatives.