Some elementary properties of semitransitive relations and ferrers relations

Semitransitive relations and Ferrers relations are binary relations which are important for fundamental discussion of utility. We consider semitransitive relations and Ferrers relations using Boolean matrices having zeros and ones as their elements. We obtain some properties of semitransitive relations and Ferrers relations by combining their well-known properties and other sufficient conditions. They show some facets of semitransitive relations and Ferrers relations and give conditions that given relations become semitransitive relations or Ferrers relations.