The sum rule states that if and are disjoint sets then $|A| + |B|$.
According to the sum rule, if are parwise disjoint sets then $|A_1| + |A_2| + ... + |A_n|$.
title: Example
A student can choose one project from project lists of three lecturers.
- John's list has 11.
- Bill's has 10.
- Eve's has 8.
No project occurs twice. How many possible projects are there to choose from?
- $A = \{ p | p \text{ is a project on John's list} \}$
- $B = \{ p | p \text{ is a project on Bill's list} \}$
- $C = \{ p | p \text{ is a project on Eve's list} \}$
Hence $|A \cup B \cup C| = |A| + |B| + |C| = 29$.