Addition principle

In combinatorics, the addition principle or rule of sum is a basic counting principle. Stated simply, it is the intuitive idea that if we have A number of ways of doing something and B number of ways of doing another thing and we can not do both at the same time, then there are ${\displaystyle A+B}$ ways to choose one of the actions. In mathematical terms, the addition principle states that, for disjoint sets A and B, we have ${\displaystyle |A\cup B|=|A|+|B|}$.

The rule of sum is a fact about set theory.

The addition principle can be extended to several sets. If ${\displaystyle S_{1},S_{2},\ldots ,S_{n}}$ are pairwise disjoint sets, then we have:

This statement can be proven from the addition principle by induction on n.