Wednesday, May 25, 2016

Relation algebra

We can establish a theory of binary relations in terms of their ordering as well as composition and transposition. The composition of binary relations generalizes the notion of composition of functions. Functional binary relations merely have a functional dependency from their input argument to the output argument. The inverse functional binary relations are their transpose. One to one binary relations are both functional and inverse functional. The composition of one to one binary relations is a one to one binary relation. Symmetric binary relations are equal to their transposition. The involutions are symmetric as well as functional. These properties allow us to better understand binary relations in terms of composition and transposition.