#10 - Local, Justify, Rule Substitution

[Emily Haney-Caron]

Hi Blair,

Great question. Answer Choice E would prevent F from being 7th, which would have an additional effect beyond the rule we're replacing.

[Oscarg104]

Hi, I am having difficulty with D being the correct answer. Wouldn't it force F into slot 1 and eliminate the possibility of being 7th, which would, in turn, alter the possible arrangement of the photographs?

[Brook Miscoski]

Oscar, D does not force F into the first slot. You can place F 7th, M 1st, and fit H<GK and (IL) into the remaining 5 contiguous spots.

What D does is to give you two scenarios--either H is between M and GK, or H is second. Let's look at those two possibilities.

If H is second, that leaves only F or M to go first--can't be (IL) or GK because of their proximity rules. GK will end up after H. All of that was also true before the second rule was deleted.

If H is between M and GK, then by definition H is not first. Additionally, you can't do GKHM, because M wouldn't be in the first three spots, so this preserves H before GK. Again, this preserves the game as it was before deleting the second rule.

By looking at the scenarios this way, you can avoid making an oversight like thinking that F is getting bumped. Break the choice down into its parts and consider them, and that will help on a difficult suspension question like this one.

[lina2020]

Hi PowerScore,

I had originally picked B but after reading through the explanation, I understand the reasoning for the correct answer choice. However, based on the most recent post on your end, it sounds like D is diagrammed as a bi-conditional which is the part that confused me. I thought that would only apply if the statement reads "if and only if" or "if but only if". With that said, please see below for my questions:

1. How would you diagram answer choice D?
"Unless Hibiscus is second, it must be somewhere between Magnolia and Gardenias."

H in 2 not ------> M/GK - H - GK/M (I diagrammed this using "if not")

Contrapositive:
H before M and K ------> H in 2
or
M and K before H ------> H in 2

2. Did I diagram that correctly? Is there an easier way to go about this in the future when it's a compound conditional statement such as this one?

3. Are there any other scenarios that would lead to a bi-conditional statement/diagram that I should look out for? Other than the two I listed above: "If any only if" and "if but only if"

[KelseyWoods]

Hi Lina!

Answer choice (D) is not a biconditional statement like you find with "if and only if" or "if but only if." Instead, it's a type of rule that we typically refer to as the "at least one" rule.

Consider this example:

If not A, then B.

Diagram: A B
Contrapositive: B A

This relationship tells us that you always have to have at least one of A or B. If A isn't there, B has to be. If B isn't there, A has to be. So there's no way to have neither A nor B. That means we always have to have at least one of A and B. We could have both A and B. But we can't have neither. When you're looking at a contrapositive pair like we have above, you can't have the two sufficient conditions at the same time (in this case, we can't have not A and not B at the same time) but you could have the two necessary conditions at the same time (it would be fine to have both A and B).

So applying that to answer choice (D):

Unless Hibiscus is second, it must be somewhere between Magnolia and Gardenias.

Diagram: H2 M/GK H GK/M
Contrapositive: M/GK H GK/M H2

(Diagramming note: You can absolutely split up the sufficient condition in the contrapositive as you did, if it makes it easier for you to understand. Your diagram is fine and whichever way of diagramming makes it easier for you to understand the relationship correctly, is the right way to diagram for you!)

Based on our analysis of "If not A, then B" above, we can see that this relationship works in the same way: if H is not 2nd, H is between M and GK. If H is not between M and GK, then H is 2nd. That means one of those two things always has to happen. We always have to have either H 2nd or H between M and GK.

Hope this helps!

Best,
Kelsey

[KCOURSEY28]

Hello,

I have read the explanations for this question however I have a question about the explanation on why "C" is incorrect. I didn't choose "C" as the correct answer but for different reasoning. I'm unsure of the importance of K not being referenced "K is not referenced (And thus it would be possible for the GK block to appear before H when H is one of the later positions)." Could someone please clarify this justification so I don't miss this type of question in the future? Thank you.

[Robert Carroll]

k,

The only rule that puts H before G or K is the rule we're trying to substitute for. So if an answer choice doesn't mention G or K, we should rightly ask "Will this answer choice put H before G and K indirectly?" The complete lack of discussion of G or K in the answer tells us that answer choice (C) does not do that, so it fails to do something we're looking for.

Robert Carroll