On the law (a�b?)?=b+a?�b? in de Morgan algebras and orthomodular lattices

Abstract

This paper's goal is to prove that the only de Morgan algebras and the only orthomodular lattices in which the law (a·b?)?=b+a?·b?, posed by Charles Elkan in [1] holds, are those that are boolean algebras. That is, that among both families of de Morgan algebras and orthomodular lattices, Elkan's formula is only characteristic of boolean algebras.