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

Welcome back. In this problem, we'd like to translate the following conjunctions from symbols to words and then determine the truth value. We have the simple statements P, 10 is a whole number, Q, 5 is less than 3, and R 2 times 7 is 14. And we'd like to translate this statement here from symbols to words, which is not P and R. So, the first part that we have here is not P. Now, the statement P is 10 is a whole number, but we need the negation of P. The negation of P would be 10 is not a whole number, so let's start there. 10 is not. A whole number. Next, we have this symbol here, which is the logical symbol for the word and, so we'll add and. And then we have R. R is the statement 2 times 7 is 14, so we can write that in, and 2. 7. Is 14 And we get the statement, 10 is not a whole number, and 2 times 7 is 14. Now, as a reminder, a conjunction is true when the two statements that we're combining are true. So, let's look one at a time. 10 is not a whole number. Well, that's false because 10 is a whole number, and we have 2 times 7 is 14. This is true as 2 times 7 is 14. But because we don't have that both of the statements we're combining together are true, we can say that overall, this conjunction is false. Great work