Translate the following conjunctions from symbols to words. Then, determine the truth value. p p : Ten is a whole number. q q q : Five is less than three. r r r : Two times seven is fourteen. q Λ p q Λ p q Λ p

Welcome back. In this problem, we'd like to translate not Q and P from symbols to words, and we've been given the simple statements for P, Q, and R. Now, let's start with not Q. We know that Q is the simple statement 5 is less than 3. So not Q should be the opposite of that, and we can get that by adding in the word not. So, not Q will be 5 is not. Less than. 3 Next, we have the logical symbol for the word and, so let's put in and. Finally, we have P, which is the simple statement, 10 is a whole number, so we can write that in next, and 10 is a whole. Number So we end up getting the statement 5 is not less than 3, and 10 is a whole number as our conjunction. Now, as a reminder, conjunctions are true when the things we're combining together are all true. Here we're combining two statements together, so we want to check if each statement is true individually, starting with 5 is not less than 3. Well, this is true, 5 is not less than 3. And then we want to look at our second statement, which is 10 is a whole number. Now, again, this is true, 10 is a whole number. So the two statements we're combining together in this conjunction are true individually, meaning that the conjunction itself is also true. Great work.