2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146249This paper is a contribution to the study of a quasi-order on the set $Ω$ of Boolean functions, the \emph{simple minor} quasi-order. We look at the join-irreducible members of the resulting poset $\tildeΩ$. Using a two-way correspondence between Boolean functions and hypergraphs, join-irreducibility translates into a combinatorial property of hypergraphs. We observe that among Steiner systems, those which yield join-irreducible members of $\tildeΩ$ are the -2-monomorphic Steiner systems. We also describe the graphs which correspond to join-irreducible members of $\tildeΩ$.10 pages, ROGICS08,Mahdia 12-15 may 2008Combinatorics05C75, 05C65, 05B05, 05B07, 06A07, 06E30, 94C10text