Binary relation

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Binary relations are used in many branches of mathematics to model a wide variety of concepts. These include, among others:

The identity element is the universal relation. For example, the relation "is divisible by 6" is the intersection of the relations "is divisible by 3" and "is divisible by 2".

In the context of homogeneous relations, a partial equivalence relation is difunctional.

The corresponding logical matrix of a general binary relation has rows which finish with a sequence of ones. Thus the dots of a Ferrer's diagram are changed to ones and aligned on the right in the matrix.

In terms of the calculus of relations, sufficient conditions for a contact relation include