Translate the following conjunctions from words to symbols. Then, determine the truth value. p p : All courses give tests. q q : Some courses give homework. r r : Some courses have textbooks. All courses don’t give homework and don’t have textbooks.

Welcome back. In this problem, we'd like to translate the conjunction, all courses don't give homework and don't have textbooks from words to symbols, and we'd like to determine its truth value. Now, just like before, we're just gonna go piece by piece, and we can see here that our first piece is all courses don't give homework. Now, looking at our simple statements, we can see that the simple statement about homework is statement Q. Some courses give homework. Now, if it is not true that some courses give homework, that would mean that no courses give homework, or that all courses don't give homework. So we can see here that our piece in the conjunction, all courses don't give homework, is the opposite of the simple statement Q, some courses give homework. So this piece here is the negation of Q or not cue. Next, we have the word and. Now the word and can be represented with this symbol here for a conjunction, so we'll put that in. And finally, we have don't have textbooks. Now, we saw this before with the previous example, where sometimes we have these sentence fragments here, if the two simple statements were combining together with the word and have the same subject. In English, we don't have to repeat that subject. So we can assume that don't have textbooks has the subject all courses. So we have all courses don't have textbooks. Well, looking at our simple statements, we can see that R is the only simple statement that refers to textbooks. So it has to be related to the simple statement R. But the opposite of R, some courses have textbooks, is going to be that all courses don't have textbooks, right? If some courses have textbooks, isn't true, that would have to mean that every course didn't have a textbook. So what we have here is the opposite of the simple statement R. So we have not R. And we can say that our conjunction is not Q and not R. Now that we've translated into symbols, we have to determine the truth value of the statement. Now, again, it is typically easier to look at the version in words when determining the truth value. For conjunctions, we need both of the statements we're combining together to be true for the conjunction as a whole to be true. So let's look at each of our statements individually. First, we have all courses don't give homework. Well, that is definitely not true. I know that I have been in courses that give homework, and I'm sure you have too. So this piece is false. Next, we have all courses don't have textbooks. Well, again, I've been in courses that have textbooks, and I'm sure you have too, so this is also false. Actually, each of our individual statements are false. So, we do not combine two true statements, meaning that our conjunction is not true. In other words, our conjunction is false. It is false that all courses don't give homework and don't have textbooks. Great work.