Venn diagram

Venn diagrams, Euler diagrams (pronounced "oiler") and Johnston diagrams are similar-looking illustrations of set, mathematical or logical relationships.

[Please: What is the difference? Both diagrams below are Venn diagrams; one is asserted also to be an Euler diagram.]

Example

The Venn diagram above can be interpreted as "set A and set B 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

• All Vs are Ts
• All Ks are Vs
• Therefore All Ks are Ts.

Functionally, Venn, Johnston, and Euler diagrams are identical, though some sources argue for their distinctness in original purpose. 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, whereas John Venn has nothing left to his name but the diagram.

External links

• LogicTutorial.com (http://www.logictutorial.com/) - interactive Johnston diagram
• Lewis Carroll's Logic Game (http://www.cut-the-knot.org/LewisCarroll/dunham.shtml) - Venn vs. Euler

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See also: Boolean algebra, Karnaugh map, Graphic organizers