This cube 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.
(The term "area" is more intuitive for the dual Venn diagrams.)

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

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

 

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