Venndiagram

A Venndiagram, more properly called a Venn diagram, is a diagrammatic tool for representing the logical relations between a finite collection of sets. It is typically drawn as overlapping closed curves, usually circles, within a rectangle that denotes the universal set. Each curve represents a set, and the regions formed by their overlaps correspond to the various possible combinations of membership. The plane is partitioned into disjoint regions, each encoding a unique pattern of inclusion or exclusion relative to the represented sets.

Operations on the depicted sets correspond to standard set operations. The intersection represents elements common to the sets; the union represents elements that belong to at least one of the sets; the complement represents elements outside a given set relative to the universal set. Regions inside a curve but outside others indicate elements in one set but not the others; overlapping regions indicate elements belonging to multiple sets.

Two-set diagrams yield up to four regions; three-set diagrams can display up to eight regions. Representing larger numbers of sets in a single planar diagram becomes increasingly difficult, and not all conceptual intersections need to be shown. Euler diagrams depict actual relationships and may omit non-existent intersections. For more than a few sets, higher-dimensional or non-circular layouts are used.

Typical uses include logic, probability, statistics, data visualization, computer science, and education, where Venn diagrams aid reasoning about unions, intersections, complements, and inclusion relations.

History: John Venn introduced these diagrams in the 1880s to illustrate propositions and logical reasoning. Since then, Venn diagrams have become a standard visual aid, with variants such as multi-set diagrams and Euler diagrams, and various digital tools for generating diagrams.