Thanks for the question! So let’s take a look at the correct answer choice, (E), and see why yams can’t be sixth.
Let’s say that we include yams in this soup. Well, take a look at the third rule. That tells us either potato’s an ingredient, or yam’s an ingredient, but not both (guess we don’t want too many starches in this soup). So we’re deciding to put yam in the soup (since if it’s not in the soup, it can’t be the sixth ingredient added in the soup since it wasn’t added in the first place). Well, that means no potatoes in the soup.
Now we’re also told that if jalapeños are an ingredient, then yam isn’t an ingredient (because we don’t like spicy yams). Well, we can diagram that
J —> ~Y
What’s the contrapositive of this? Well, it’s that
Y —> ~J
In other words, if we have yams, we don’t have jalapeños. But hold on. We got rid of potatoes, and we also got rid of jalapeños. We started off with seven vegetables originally. Getting rid of two of them means that we have at most five vegetables left! So it’s impossible to have yams in a six-ingredient soup (in fact, there’s only one way to have a six-ingredient soup, and that’s if yams are the only thing we leave out), and that’s why (E) is the correct answer choice.
Hope this helps! Feel free to ask any other questions that you might have.
cacostelloon September 28, 2020
Oh my gosh! What a trick question.... that's right if there are only 5 vegetables left than you cannot have a sixth ingredient... I'm feeling so Homer Simpson right now.
