Definition:Euler Diagram

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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:

(a) The subset relation $T \subseteq S$
(b) Examples of disjoint sets $S \cap T = \O$
(c) The most general case: $S \cap T \ne \varnothing$, $T \nsubseteq S$, $S \nsubseteq T$
EulerDiagrams2Sets.png

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


Source of Name

This entry was named for Leonhard Paul Euler.


Also known as

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


Sources