Venn diagrams (top) and Euler diagrams (bottom) of relations corresponding to 3-ary Boolean functions
Areas marked black contain no elements. Euler diagrams avoid showing empty areas, but this is not always possible.

See also: v:User:Watchduck/Logic#3-ary relations

Each function belongs to one of  A000616(3) = 22 big equivalence classes (becs).
Relations from complementary becs are ordered symmetrically to the vertical middle axis of the image - except in rectangle 4: All relations with 4 white areas are from self complementary becs.

Each one of the 256 possible relations can be expressed by one of these Euler diagrams by permuting and negating the arguments A, B, C.
E.g. can be expressed by .

The beige numbers denote the number of white areas in the diagrams in the corresponding beige rectangle.
(That is the number of ones in the corresponding Boolean functions.)

 A039754