1. Daniel da Silva Márcio Édi Araújo da Costa Nº15 9ºB Flávio André Sousa Faria Nº9 9ºB

2. Daniel da Silva Daniel da Silva (16 May 1814 – 6 October 1878) was a Portuguese mathematician and marine officer. He was born in Lisbon. He completed his first studies at the Portuguese Royal Naval Academy, and then proceeded his education in Mathematics at the University of Coimbra where he became a doctor. The inclusion-exclusion principle is sometimes attributed to Silva, which was included in a 1854 publication. However, the result is normally attributed to Abraham de Moivre.

3. The Inclusion-Exclusion Principle In combinatorics (combinatorial mathematics), the inclusion– exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets, where A and B are two finite sets and |S| indicates the cardinality of a set S (which may be considered as the number of elements of the set, if the set is finite). The principle is more clearly seen in the case of three sets, which for the sets A, B and C is given by this formula: