# Studies of Euler diagrams/examples

dummy

## miniri

This is a filtrate of barita. See here.

## medusa

A good Euler diagram of this Boolean function needs 3 dimensions.

## barogi

This representation is inflated. The Boolean function is sufficiently represented by the red-yellow Euler diagram (A, D).
The green-blue Venn diagram (B, C) does not add information. But the corresponding circles e.g. in barita are relevant. So are those in the gap variants vidita and vanatu.

## bareto

This is like barogi shown above, but with the additional information, that B and C are complements:     $(A\cap D=\varnothing )\land (B^{c}=C)$ .
This is a 4-ary Boolean function, whose bloatless part is the 2-ary barogi.   (It is a special case, that the arguments of the bloatless and bloat part are disjoint.)

## basori

This representation is also inflated. Only the red-yellow-brown Euler diagram (A, D, E) matters.
The green-blue Venn diagram (B, C) does not add information. But the corresponding circles in basiga are relevant.

## barita

The green-blue (B, C) and brown-magenta (E, F) Venn diagrams would be separate bundles, if they were not trisected by the red-yellow Euler diagram (A, D).
In the graph this is a multiplication, and in the formula it is a conjunction. Compare the filtrates.

## basiga

Without the small bundle (F, G, H) the surrounding one would be just the red-yellow-brown Euler diagram (A, D, E), as in basori.
But as the small bundle is only in B, and not in C, the green and blue circles are also needed.

If the inner bundle were on its own, it would fall apart into the circles F and H. The circle G would just bisect that Boolean function, adding no information. But in the nested bundle, the circle G is relevant. Removing it would mean, that G implicitly bisects the whole Boolean function (including A...E). But actually it bisects only one cell of the surrounding bundle, namely the one where only B and D intersect.

Compare the gap variants and filtrates.

## dukeli

This graph is like the matrix graph above, without vertex 9. It is drawn on a sphere in an attempt to create a "good" graph with a convex outline.
The parallelity of great circles is sufficiently vague, to allow three collinear edge pairs, while edges of the same color are still parallel.