Translate the following disjunctions from symbols to words. Then, determine the truth value. p p : Dogs purr. q q q : Mice squeak. r r r : Wolves howl. ~ p p V V V ~ q q q

Welcome back. In this problem, we'd like to translate not P or not Q from symbols to words and determine the truth value. So let's begin starting with not P. Now, P is the simple statement dogs purr. So not P is the opposite of that, which is dogs don't purr. Then we have this symbol here, which is the logical symbol for the word or, and then we have not q. Now q is mice squeak, so not q is the opposite, which is mice don't. Squeak. So we get the disjunction, dogs don't purr or mice don't squeak. Now, we want to determine the truth value, and as a reminder, disjunctions are true when at least one of the statements we're combining together is true on its own. So let's check each of these statements individually and make sure at least one of them is true. Now first we have dogs don't purr. Now that is true, dogs don't purr. And after that we have mice don't squeak, and that is false because mice do squeak. So we have one true statement that we're combining with one false statement. Now, because at least one of our statements is true on its own, we can say that the disjunction is true. So it is true that dogs don't purr or mice don't squeak. Great work.