Studies of Euler diagrams/filtrated boolf

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To filtrate a Boolean function means to reduce its information about many sets to those of interest.
Graphically it means removing circles from the Euler diagram and treating all merged cells as true, if any of the component cells are true.

Rdr.svg medusa[edit | edit source]

BCD (A removed)

The result is a 3-circle Venn diagram without gapspots, i.e. the tautology.

EuDi; medusa remove a.svg EuDi; 4-ary 22527; crosses; triple 1 2 3.png

Rdr.svg bazinga[edit | edit source]

The 8 sets create 21 cells.

Rdr.svg doguva[edit | edit source]

Like bazinga above, but 3 of the 21 cells are gaps, leaving 18 true cells.

simple filtrates (without images)[edit | edit source]

Leaving only ABC results in a 3-circle Venn diagram with a gapspot in the center.
Leaving only BCD results in one without a gapspot, i.e. the tautology.

B or C removed (each bordering a gapspot)[edit | edit source]

Both B and C border all the three gapspots. Removing them merges the gapspots with their full neighbors.
These filtrates of doguva are the same as the equivalent filtrates of the gapless bazinga shown above.

pairs of sets removed (leaving single gapspot)[edit | edit source]

BCDEFH (AG removed)
EuDi; batch 5; 5.svg
EuDi; doguva remove ag.svg
13 true cells + 1 gap