Binary relation

Relationship between elements of two sets

In mathematics, a binary relation associates some elements of one set called the domain with some elements of another set (possibly the same) called the codomain. Precisely, a binary relation over sets X and Y is a set of ordered pairs (x,y), where x is an element of X and y is an element of Y. It encodes the common concept of relation: an element x {\displaystyle x} is related to an element y {\displaystyle y} if and only if the pair ( x , y) {\displaystyle (x,y)} belongs to the set of ordered pairs that defines the binary relation. An example of a binary relation is the "divides" relation over the set of prime numbers P {\displaystyle \mathbb {P} } and the set of integers Z {\displaystyle \mathbb {Z} } , in which each prime p {\displaystyle p} is related to each integer z {\displaystyle z} that is a multiple of p {\displaystyle p} , but not to an integer that is not a multiple of p {\displaystyle p} .

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