Robert's Mistakes

Diagram 4: Venn-, Euler- and spidergramm

Jul 15, 2013

Venn diagrams have been popular to teach elementary set theory so you probably have seen one in school. One for order n shows all 2^n intersection sets. So all Venn diagrams of order n describe the same structure. Wikipedia has images up to order 6, some suggested by Venn himself:

http://en.wikipedia.org/wiki/Venn_diagram#Edwards.27_Venn_diagrams

Henderson proved in 1963 that you can find symmetric Venn diagrams of order n only if n is a prime number. Here's a beautiful one for order 11 which has been found only recently by Khalegh Mamakani und Frank Ruskey:

http://arxiv.org/abs/1207.6452

An Euler diagram is similar but only shows the subsets one is interested in. By leaving the uninteresting parts out one can highlight some subsets and interpret these as a boolean formula (with AND).

http://en.wikipedia.org/wiki/Euler_diagram

Now to get a spidergramm, add dots connected by lines to indicate disjunction (OR). If you place multiple spiders you get multiple formulas. Since you can also mark the outside of any set (using multiple points if necessary) you can construct negations (NOT), too.

http://en.wikipedia.org/wiki/Spider_diagram