Chaiwat Namnak, Ratsiri Sanguanwong, Left Cancellative and Right Cancellative Elements of Semigroup of Relations, BMSA Volume 2, Bulletin of Mathematical Sciences and Applications (Volume 2) https://www.scipress.com/BMSA.2.38 Abstract: Let <i>R(X)</i> denote the set of all relations on a set <i>X</i>. Then <i>R(X) </i>becomes a semigroup under composition. The purpose of this paper is to describe the element of <i>R(X)</i> which is left cancellative and right cancellative. Keywords: Left Cancellative Element, Right Cancellative Element, Semigroup of Relations