Augustus DeMorgan (1806-1871), the British mathematician and logician, contributed what we now call DeMorgan's Laws to the science of logic. These laws allow the substitution of one statement for another logically equivalent statement. There are two pairs of statements that operate according to DeMorgan's law, and each statement in a pair means, logically speaking, the same thing as its partner. These laws are helpful in making valid inferences in proofs of deductive arguments, and the laws are based on the concept of logical equivalence and the logical functions of the connectives "not," "and," and "or." There are other statements that are logically equivalent and used in deductions, but DeMorgan's laws employ and clarify quantificational relationships moreso than do other equivalence rules.

To assert that two statements are logically equivalent means that they share the same truth values in every possible instance. The concept of logical equivalence...