File:Logic matrix - whatsthecaserelations.svg

Summary[edit]

Relations like the subset relation are true in several cases. Such cases are shown here.

15 cases are possible, when there are 2 sets, and the question is only, if an area is empty or not.

The case that all areas are empty can be regarded as impossible, because this would mean an empty universe.
(Where the complement of the empty set would be the empty set itself.)

The Venn diagrams in this matrix are like those representing syllogisms - apart from the fact that all areas are defined as "there is something" or "there is nothing", while in the syllogism graphics some areas are undefined:

See also: Template:Operations and relations in set theory and logic

Other version:

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