# 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.

## Examples

The following examples show:

- $(\text a)$ The subset relation $T \subseteq S$
- $(\text b)$ Examples of disjoint sets $S \cap T = \O$
- $(\text c)$ The most general case: $S \cap T \ne \O$, $T \nsubseteq S$, $S \nsubseteq T$

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

## Also known as

Some sources refer to a **Euler diagram** as **Euler's circles**.

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.

## Also see

## Source of Name

This entry was named for Leonhard Paul Euler.

## Sources

- 1965: A.M. Arthurs:
*Probability Theory*... (previous) ... (next): Chapter $1$: Set Theory: $1.2$: Sets and subsets

- (where this is referred to as a Venn diagram)

- 1965: J.A. Green:
*Sets and Groups*... (previous) ... (next): $\S 1.2$.Subsets: Example $10$

- (where this is referred to as a Venn diagram)

- 1972: A.G. Howson:
*A Handbook of Terms used in Algebra and Analysis*... (previous) ... (next): $\S 2$: Sets and functions: Sets - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**Euler's circles**