A Boolean algebra is a set with two binary operations, and , that are commutative, associative and each distributes over the other, plus a unary operation . One interpretation of Boolean algebra is the collection of subsets of a fixed set X .
Equality here means the usual equality of sets.
Another interpretation is the calculus of propositions in symbolic logic. In this setting equality means logical equivalence. It is not surprising then that we find analogous properties and rules appearing in these two areas. For example, the axiom of the distributive properties says that for sets we have while is a familiar equivalence in logic. The following table contains just a few rules that hold in a Boolean algebra, written in both set and logic notation.