Discrete Mathematical Structures by Pearson

Set Theory 1-11

1.2.11 The Inclusion and Exclusion Principle

Whenever two or more tasks are performed simultaneously, then the usual sum and product

rules cannot be used. In the case of two tasks, if we add the number of ways in which each

task is performed, then the number of ways to perform both the tasks is counted twice. In order

to correct this double counting and find the number of ways of doing either of the tasks, the

number of ways of performing each task is added, that is, inclusion and the number of ways of

performing both the tasks is subtracted from this sum, that is, exclusion. This method of counting

is called the principle of ...