Euler diagram
The elementary operations upon and relations between classes — complementation, logical sum, logical product, class equality, class inclusion — may sometimes advantageously be represented by means of the corresponding operations upon and relations between regions in a plane. (Indeed, if regions are considered as classes of points, the operations and relations for regions become particular cases of those for classes.) By using regions of simple character, such as interiors of circles or ellipses, to stand for given classes, convenient diagrammatic representations are obtained of the possible logical relationships between two or more classes. These are known as Euler diagrams, although their employment by Euler in his Letters to a German Princess (vol. 2, 1772) was not their first appearance. Or the diagram may be so drawn as to show all possible intersections (2n intersections in the case of classes), and then intersections known to be empty may be crossed out, and intersections known not to be empty marked with an asterisk or otherwise (Venn diagram). — A.C.