EQUIVALENCE

We say that two strings are equivalent when they have exactly the same truth value (meaning that that when one is true the other is true, or that when one is false the other is false). The signal B expresses this relationship, and it is the way we symbolize English statements using the phrase if and only if, which tells us that one thing is both a necessary and a sufficient condition for another.

The truth table is as follows:
P Q || PQB
T T........T
T F........F
F T........F
F F........T

The string PQB is itself equivalent to PQCQPCA as well as PNQOPQNOA.

One advantage of knowing which strings are equivalent is that we are able to substitute equivalent modules in any string without affecting its truth value. For instance, since PNQO and PQC are equivalent, we can rewrite PQCRC as PNQORC. Using the same principle, we could also have PQCNRO and PNQONRO, and, given the equivalence of PQCN and PQNA as well as of PQON and PNQNA, we could turn both into PQNARO (the disjunctive normal form).

Return to variables and signals.

Go back to the starting page.