& Q) with the corresponding sentence ~ P v ~ Q, and vice versa, that i - PDF document

& Q) with the corresponding sentence ~ P v ~ Q, and vice versa, that is, it allows us to replace a sentence of the form ~ P v ~ Q with the corresponding sentence ~(P & Q). Of course, DeMorganÕs rule also allows us to replace a sentence of the form ~ (P v Q) with the corresponding sentence ~ P & ~Q, and vice versa. Notice that DM ÒdrivesÓ the tildes inside, that is, in these cases, it shifts the tilde from the outside of the brackets onto the inside letters. At the same time, the wedge changes to the ampersand or the ampersand changes to the wedge, of course. An algorithm is a very precise, step-by-step procedure for carrying out a specific task. The purpose of this supplement is to present is means that one may replace the other anywhere in a proof. (This equivalence can easily be confirmed on a truth-table, by the way, if you studied Chapters 14 B) we get: ( ~A v ~ B). (We removed the double tildes on the outside of the brackets.) Now we can say: ~(A & B) is equivalent to ~A v ~B. This means that one formula may replace the other anywhere in a proof. Notice that the DM algorithm, in this case, gives the same result as the original DeMorganÕs rule. Here are additional examples. In each of the following, the second formula was derived from the first by applying the The Many Worlds of Logic