File:Relation 0101 1010.svg

This Venn diagram represents a 3-ary Boolean relation that makes only universal quantifications,
i.e. that tells only that somewhere, namely in the black areas, are no elements.

In the following example calculation the 3-ary relations are represented by their "logical tensors",
Venn diagrams like this one and cubes dual to the Venn diagrams:

${\displaystyle A\subseteq B}$	${\displaystyle \land ~}$	${\displaystyle B\subseteq C}$	${\displaystyle \Leftrightarrow }$	${\displaystyle A\subseteq B\subseteq C}$
1011 1011	${\displaystyle \land ~}$	1100 1111	${\displaystyle \Leftrightarrow ~}$	1000 1011

The following representations of syllogisms also use this kind of Venn diagram.
The representation of Modus Barbara shows the same content as the example calculation above,
although the Venn diagrams are turned counterclockwise by 60°:

 

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