Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

## Venn Diagram

Venn diagrams have been introduced around 1880 by John Venn and are a simple but effective method of visualizing the sample space and its individual events. Furthermore, Venn diagrams can be used to display logical operations on sets, such as unions, or intersections.

A Venn diagram consists of a frame which represents the population P, and one ore more arbitrarily formed, closed shapes which are contained in P representing partial sets to be displayed. The negation of the partial set A (complementary set A') is equal to the outer area of the set within the boundaries of P.

The Venn diagrams illustrate some axioms of Boolean algebra in quite a natural form, as any combination of sets can be formed by putting them on top of each other. The resulting regions can be interpreted as logical AND or logical OR.