How did John Venn use diagrams to show relationships between classes?

John Venn introduced his eponymous diagrams as a graphical method to represent relations of inclusion and exclusion between classes or sets. By using intersecting circles, he provided a visual tool to analyze categorical propositions and test the validity of categorical syllogisms.12

In these diagrams, each circle represents a class and is labeled with an uppercase letter. Venn utilized specific visual markers to denote the status of class members:12
* Shading: Used to indicate the nonexistence of members in a specific area (e.g., shading an intersection to show that no members exist in that combined class).12
* Lowercase x: Placed within a section to indicate the existence of at least one member of a given class.12

By diagramming the premises of a syllogism—typically starting with universal premises—one can determine if the conclusion is represented in the final figure. If the conclusion is present, the argument is valid; if not, it is invalid. Venn detailed this method in his 1881 work, Symbolic Logic.12