Venn diagram
Venn diagrams, Euler diagrams (pronounced "oiler") and Johnston diagrams are similar-looking illustrations of set, mathematical or logical relationships.
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The Venn diagram above can be interpreted as "the relationships of set A and set B which may have some (but not all) elements in common".
The Euler diagram above can be interpreted as "set A is a proper subset of set B, but set C has no elements in common with set B.
Or, as a syllogism
Example
Venn, Johnston, and Euler diagrams may be identical in appearance. Any distinction is in their domains of application, that is in the type of universal set that is being divided up. Johnston's diagrams are specifically applied to truth values of propositional logic, whereas Euler's illustrate specific sets of "objects" and Venn's concept is more generally applied to possible relationships. It is likely that the Venn and Euler versions have not been "merged" because Euler's version came 100 years earlier, and Euler has credit for enough accomplishment already.
The difference between Euler and Venn may be no more than that Euler's try to show relationships between specific sets, whereas Venn's try to include all possible combinations. With that in mind:
There was some struggle as to how to generalise to many sets. Venn got as far as four sets by using ellipses:
- three sets:
- four sets:
- five sets:
- six sets:
John Venn was a 19th-century British philosopher and mathematician who introduced the Venn diagram in 1881.
A stained glass window in Caius College, Cambridge, commemorates his invention.
Origins
External links
See also: Boolean algebra, Karnaugh map, Graphic organizers