The principle of inclusion and exclusion and its applications

In this BSc thesis we focus on the principle of inclusion and exclusion and its applications. This principle is a combinatorial tool for counting. More precisely, it is a tool that allows one to determine the cardinality of unions of finitely many finite sets. To do so one needs to be able to determine the cardinality of each of the sets and their (multiple) intersections. In the thesis we introduce same basic notions in combinatorics, present some simple facts and give examples of applications. We illustrate the principle of inclusion and exclusion on a simple problem. We give a mathematically correct proof of the theorem. In the remainder of the thesis we give a few demonstrations of the principle of inclusion and exclusion in use. Specifically, we consider to the Stirling numbers of the second kind, the Euler φ function and the game Scrabble