Within propositional logic, the term equivalence is used in either of the following two ways: (1) as a particular type of propositional statement or (2) as the logical operator used to form an "equivalence" statement. In order to develop a precise definition of equivalence, some background regarding propositional logic is necessary. The Greek philosopher Aristotle (384 b.c.-322 b.c.) provided the first systematized approach to propositional logic. Keep in mind that logic at that time was expressed entirely in ordinary language and not at all symbolically. Nevertheless, "Aristotelian logic" was, and remains, the starting point to formal logic. Within the Aristotelian system the concepts of "proposition" and "truth" are of paramount importance. A proposition (also called a statement) is defined as a linguistic formation used to communicate information that may be labeled as "true" or "false". Moreover, there exist several principles related to propositions: the principle of identity states...