ON THE SEMIGROUP OF DIFUNCTIONAL BINARY RELATIONS - Ibrahim, Muhammad Jamilu; Sawudi , Ibrahim Mamman; Imam, Abdussamad Tanko (FUDMA JOURNAL OF SCIENCES, 2022)
In this paper, we have examine some properties of elements of the semigroup , where DX, is the set of all binary relations Î± âŠ† X Ã— X satisfying , (), and is a binary operation on DX defined by () , with xÎ± denoting set of images of x under Î±, and yÎ²âˆ’1 denoting set of pre-images of y under Î². In particular, we showed that in the semigroup  there is no distinction between the concepts of reflexive and symmetric relations. We also presented a characterization of idempotent elements in  in term of equivalence relations.
Keywords: Binary relations, Cardinalities, Difunctional relations, Green’s relations