Falsehood preserving boolean formulas

The particular class of falsehood preserving boolean formulas is of some interest to us, because it can be expressed with differences rather then with complements. So we can apply them to sets without having to deal with or define their complements. The most basic falsehood preserving logical connectives in set theory are the constant empty set and the identity. Beyond that there is union, intersection, difference, and symmetric difference which are among the four most important logical connectives in set theory. All of them are falsehood preserving because they do not take anything from the complement. They can be expressed with union, intersection, and difference without reference to complements. The symmetric difference is merely the difference between the union and the intersection. Other boolean formulas can be expressed using complements, when necessary, but it is useful to be able to express set theoretic operations without defining them.