# Studies of Euler diagrams/filtrated boolf

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.

## medusa[edit | edit source]

original ABCD | |
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The four sets create 13 cells. | |

BCD (A removed) | |
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The result is a 3-circle Venn diagram without gapspots, i.e. the tautology. | |

ABD (C removed) | |
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The result shows all intersections except that of all three circles. | |

## bazinga[edit | edit source]

The 8 sets create 21 cells.

ABDEFH (CG removed) | |
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original |
10 cells |

ACDGH (BEF removed) | |
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original |
9 cells |

## 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.

ACDEFG (B removed) | |
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original |
13 cells |

ABDEFG (C removed) | |
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original |
13 cells |

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

ABCDGH (EF removed) | |
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original |
14 true cells + 1 gap |

BCDEFH (AG removed) | |
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original |
13 true cells + 1 gap |