Addition principle

alt=A collection of five dots and one of zero dots merge into one of five dots.|thumb|193x193px|5+0=5 illustrated with collections of dots.

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 <math>A + B</math> ways to choose one of the actions. as can be seen with the previously mentioned equation for the union of disjoint sets A and B being equal to |A| + |B|.

The addition principle can be extended to several sets. If <math>S_1, S_2,\ldots, S_n</math> are pairwise disjoint sets, then we have: To prove this, notice that <math>|A^c| + |A| = |S|</math> by the addition principle.

The addition principle can also be used to prove the multiplication principle.