A Note on the Historical Development of Logic Diagrams: Leibniz, Euler and Venn

Abstract

Lessons on sets have become commonplace in schools today. Venn diagrams proliferate and, even in primary schools, children can be seen sorting and classifying objects by size, colour and shape and placing them in spaces marked out on the floor by chalk outlines or wooden hoops. Older children learn that such diagrams are named after the English logician, John Venn, and that through them we can represent the relations of membership and inclusion and the operations of union, intersection and complementation. A rectangle is drawn to represent the universe U: subsets of U are represented by the interiors of circles, or other closed curves within U, i.e. subspaces of the rectangle. The elements of U are represented by points within the rectangle, the elements of a subset A by points within the corresponding subspace of the rectangle and the elements of A′ by points within the rectangle but outside the region representing A.