Binary relation

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Binary relation

In mathematics (specifically set theory),
a binary relation over sets X and Y is
a subset of the Cartesian product X × Y; that is,
it is a set of ordered pairs (x, y) consisting of elements x in X and y in Y.[1]

It encodes the common concept of relation:
an element x is related to an element y, if and only if the pair (x, y)
belongs to the set of ordered pairs that defines the binary relation.

A binary relation is the most studied special case n = 2 of
an n-ary relation over sets X1, ..., Xn,
which is a subset of the Cartesian product X1 × ... × Xn.[1][2]