sentences:  Though symmetric skew lattices might not be.In a sense they reveal the independence between the properties of symmetry and distributivity.A zero element in a skew lattice S is an element 0 of S such that for all formula_187 formula_188 or, dually, formula_189 (0)
  
  A Boolean skew lattice is a symmetric, distributive normal skew lattice with 0, formula_190 such that formula_148 is a Boolean lattice for each formula_192 Given such skew lattice S, a difference operator \ is defined by x\ y = formula_193 where the latter is evaluated in the Boolean lattice formula_194 In the presence of (D3) and (0), \ is characterized by the identities