The subject of Boolean subtraction and division first appeared in the gem Laws of Thought by George Boole of Great Britain. However, this subject has been exiled from the famed Boolean algebra because it was supposed that it leads to illogical expressions. A paper recently published elsewhere by the author reintroduced the subject by clarifying it and then furnishing an application of it in the design of digital circuits. The goal of this work is to demonstrate how these banished logical operations can be employed in furnishing infallible information about blood typing and cross-matching during blood transfusion.