I have 50 pairs of socks of which 30 are black and 35 are cotton. How many pairs of socks are black and cotton? If I call the set of black socks A and the set of cotton socks B, we are looking at |A ∩ B|. It is not hard to see that: |A ∪ B| = |A| + |B| − |A ∩ B| because every element that belongs to both A and B is counted twice by |A|+|B|, so we subtract the size of the intersection once. Ther...

Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the pre...

Twenty-eight odontogenic abscesses were examined for the presence of black-pigmented Bacteroides spp. Of the 28 samples, 26 were found to contain one or more species of black-pigmented Bacteroides. Abscesses were divided into three categories according to the tissue of origin: endodontal, periodontal, and pericoronal. Four abscesses which developed after extraction were also examined. It was fo...