2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98623On every set A there is a rigid binary relation, i.e. such a relation R that there is no homomorphism (A,R)->(A,R) except the identity (Vopenka et al. [1965]). We state two conjectures which strengthen this theorem. We prove these conjectures for some cardinalities.3rd version, minor changes, PostScript, submitted to Aequationes MathLogicCombinatorics03E05 (Primary), 08A35 (Primary)text