Class algebra

There are several equivalent definitions for Class Algebra in the literature. One of them was given by the late Irving M. Copi. An equivalent definition is given here. Let C be a Mathics/class. Let ∪ and ∩ be binary operations on C and let 0 and 1 be elements of C. Then
 * (C, (∪,∩), ~, (0,1)) is_a class_algebra

if_and_only_if
 * ((C, ∪, ~, 0), (C, ∩, ~, 1)) is_a Mathics/semiclass_algebra and ((C, ∩, ~, 1), (C, ∪, ~, 0)) is_a Mathics/semiclass_algebra.