Studies of Euler diagrams/examples
miniri
[edit  edit source]Euler diagram (with separated cell 0)  

Euler diagram (cylindric)  

graph  

This is a filtrate of barita. See here.
A good Euler diagram of this Boolean function needs 3 dimensions.
Euler diagram (with separated cell 0)  

Euler diagram (cylindric)  

graph  

Euler diagram (3D)  

Venn diagram of the complement (3D)  


barogi
[edit  edit source]This representation is inflated. The Boolean function is sufficiently represented by the redyellow Euler diagram (A, D).
The greenblue 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.
Euler diagram  

graph  

planes (3D dual to the graph) 

bareto
[edit  edit source]This is like barogi shown above, but with the additional information, that B and C are complements: .
This is a 4ary Boolean function, whose bloatless part is the 2ary barogi.
(It is a special case, that the arguments of the bloatless and bloat part are disjoint.)
basori
[edit  edit source]This representation is also inflated. Only the redyellowbrown Euler diagram (A, D, E) matters.
The greenblue Venn diagram (B, C) does not add information. But the corresponding circles in basiga are relevant.
Euler diagram  

graph  

barita
[edit  edit source]The greenblue (B, C) and brownmagenta (E, F) Venn diagrams would be separate bundles, if they were not trisected by the redyellow Euler diagram (A, D).
In the graph this is a multiplication, and in the formula it is a conjunction. Compare the filtrates.
Euler diagram and graph  

layers of 3D Euler diagram  

The 3dimensional Euler diagram has 3*7 = 21 cells, 3*8 + 2*7 = 38 faces, 22 edges and 4 vertices.
The edges and vertices are two times the arrangement seen here. Compare bar.  
formula tree 

((!b and !c) or (!e and !f)) and !(a and d) 
basiga
[edit  edit source]Without the small bundle (F, G, H) the surrounding one would be just the redyellowbrown 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.
Euler diagram and graph  

formula tree 

putuki
[edit  edit source]Euler diagram (matrix) graph  

Compare piferi, where spot 0 is a gap. 
Euler diagram (cylinder) formula tree  

This Euler diagram is similar to that of dukeli below. 
!(a and c) and !(b and d)

Venn diagram of the complement (3D)  

The complement of putuki is . The Venn diagram is easily recognized as a union of two lenses.  

dukeli
[edit  edit source]This is like putuki without spot 9. For the NP equivalence class see dukeli NP. For a conversion example see dukeli and netuno.
Venn diagram of the complement (3D)  

The complement of dukeli is . The Venn diagram is easily recognized as a union of three lenses.  
