32 agnieszka julia marasik

Abstract:  The article [1] provides the terminology and notation for this paper. 1. General lattice We follow the rules: L will be a lattice and X, Y, Z, V will be elements of the carrier of L. Let us consider L, X, Y. The functor X \Y yielding an element of the carrier of L is defined by: (Def.1) X \ Y = X ? Y c. Let us consider L, X, Y. The functor X -. Y yields an element of the carrier of L and is defined by: (Def.2) X -. Y = (X \ Y) ? (Y \ X). Let us consider L, X, Y. Let us observe that X = Y if and only if: (Def.3) X ? Y and Y ? X. Let us consider L, X, Y. We say that X meets Y if and only if: (Def.4) X ? Y ? = ?L. We introduce X misses Y as an antonym of X meets Y. We now state a number of propositions: (1) X ? X ? Y and Y ? X ? Y.