 Another example of the need for caution when working with partial algebras is  how important it was that Boole chose the fundamental operation minus to be  binary subtraction, and not the unary operation of additive inverse that is  standard in ring theory. Note that the standard operations union, symmetric difference, intersection  and complement of the Boolean algebra of classes are definable in Boole’s partial-algebra by totally defined terms—he used these to be able to express propositions about classes by equations: