Definition:Euler Diagram

Definition

An Euler diagram is a graphical technique for illustrating the relationships between sets.

It differs from a Venn diagram in that whereas the latter illustrates all possible intersections between a number of general sets, an Euler diagram depicts only those which are relevant for the situation being depicted.

Note that the term Venn diagram is frequently encountered where Euler diagram would be more accurate. Ultimately it doesn't really matter, as these diagrams have no greater purpose than to provide an illustrative clarification. They cannot be used for rigorous proof.

Examples

The following examples show:

(a) The subset relation $T \subseteq S$

(b) Examples of disjoint sets $S \cap T = \varnothing$

(c) The most general case: $S \cap T \ne \varnothing$, $T \nsubseteq S$, $S \nsubseteq T$

The shape of the areas is irrelevant, but usually circles are used.

Source of Name

This entry was named for Leonhard Paul Euler.

Sources

• J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 1.2$: Example $10$ (where this is referred to as a Venn diagram)