#6 - Global, Rule Substition

[Administrator]

Please post your questions below!

[AWash180]

Hello!

I originally picked B for this question because if R is 1st then it is true that T must be 7th since there are only two places for T to go according to the 3rd rule.

Is E the correct answer because T must be the sufficient condition and R must be the necessary condition in order to replicate all of the impacts of the 4th rule?

Thanks!

[Rachael Wilkenfeld]

Hi Awash,

For this one, we want something that forces R to be in 1 whenever T is not in 1. When is T not in 1? When T is in 7. We could rewrite the rule to say when T is in 7, R is in 1. As I read the question, that would be my strong prephrase.

Answer choice (B) is the mistaken reversal of the rule we want. It says if R is in 1, T is in 7. That's true if anyone is in 1, since T has to be in either 1 or 7. We need something that tells us when T is in 7, R must be in 1. That's what answer choice (E) does.

Hope that helps!
Rachael

[apurva_98]

Hi!

When doing this question originally, I realized that the new rule would need to force R into 1 when T is not there so I eliminated everything but A and E. I ended up picking E because it was a conditional and closest to the original rule. Can someone explain why A is incorrect?

Thanks!

[Ryan Twomey]

Hey Apruva,

So I have a really specific method for substitution questions. In a substitution question, the correct answer must be two things:

1. The correct answer must be true in our original game. Aka the correct answer would be a correct answer choice in a must be true question. Aka the correct answer choice cannot give us any new conditions that did not have to be true in our original game.

2. The correct answer choice must give us our rule back.

Students always forget to do step 1.

Answer choice A states, Refrigerators must be on sale during the first week or the 7th week. This does not have to be true. This gives us a new condition. Refrigerators could be on sale during the 2nd week in our original game, so this is giving us a new condition, thus not perfectly substituting our rule.

If you incorporate step 1 into your substitution questions, you will have a much easier time with substitution questions and be less confused.

I really hope this helps, and I wish you all of the luck in your studies.

Best,
Ryan

[Areohn]

Hi,
So I originally got B and for the same reasons that Awash states below. I read the explanation that was given, but in my blind review I wrote out the same explanation as OP. I just want to know if this wording is sufficient to eliminate an answer choice moving forward. That is: Does this sufficient condition in the original rule must remain the sufficent condition in the Rsub?

I think I am a little unclear because you said that B is wrong because whenever any variable is in 1st we know that T is 7th, but given that the choice specifically states R, I am not confident that a similar AC wouldn't be appealing to me in the future.

Hello!

I originally picked B for this question because if R is 1st then it is true that T must be 7th since there are only two places for T to go according to the 3rd rule.

Is E the correct answer because T must be the sufficient condition and R must be the necessary condition in order to replicate all of the impacts of the 4th rule?

Thanks!

[Jeremy Press]

Hi Areohn,

Both you and Awash are thinking too narrowly about the "effects" of the new rule in answer choice B. It's true that one of the effects of that rule looks similar to things that had to happen under the original structure of the game (and with the original rule in place).

But there's a broader effect of the new rule you're both forgetting to consider: the new rule you put in place cannot be too permissive. In other words the new rule cannot have the effect of allowing something to happen that the original rule would've prevented from happening.

The rule in answer choice B would allow you to put both refrigerators AND televisions somewhere other than space 1. That's because the rule in answer choice B only "triggers" when refrigerators ARE in space 1. When refrigerators are NOT in space 1, the rule in answer choice B would still allow you to put televisions in space 7 (because a necessary condition can happen whether or not its sufficient condition happens). That possibility (R not in 1, T in 7) is NOT allowed under the original rule. The original rule told us that when T is not in 1 (i.e. when T is in 7), R MUST be 1. That proves answer choice B is too permissive.

That question of whether the rule in the answer "permits" something different than the original rule permitted is often the key to eliminating answer choices in these questions. It's something you should always ask.

I hope this helps!

[g_lawyered]

Hi P.S.
I wrote rule 4 & combined inference from rule 3 as:
T NOT in 1 (this means T is in 7 because of rule 3) Rule in 1
CP: R not in 1 (R open to go anywhere else) T in 1
For this reason, I understood that the answer choice to rule sub. question had to have the same effects as T being in either 1 or 7.

With this analysis, I had (C) & (D) as answer contenders:
(C) Diagrammed: R NOT 7 (R open to go anywhere else) T in 7.
CP: T NOT IN 7 (this means T is in 1 because of rule 3) R in 7
This forces T to be in 1 or 7.

(D) T IN 7 R NOT IN 7
CP: R IN 7 T NOT IN 7 (this means T is in 1 because of rule 3)
This also forces T to be in 1 or 7.

Did I misunderstand the meaning of rule 4? I don't understand why (C) & (D) are incorrect. I thought (E) introduced a new condition as if R isn't in 1, R can go anywhere (didn't want to make a mistaken reversal of R's limitation). What makes (E) the correct answer choice?

Thanks in advance!

[Robert Carroll]

g_lawyered,

I'll break up your post and reply to each point in turn!

I wrote rule 4 & combined inference from rule 3 as:
T NOT in 1 (this means T is in 7 because of rule 3) Rule in 1
CP: R not in 1 (R open to go anywhere else) T in 1

That is absolutely correct.

For this reason, I understood that the answer choice to rule sub. question had to have the same effects as T being in either 1 or 7.

This is already a bit of an issue - what you're saying here is the 3rd rule. We're substituting for the 4th rule. The 3rd rule will always be in play anyway, so there's no need to substitute for it or to choose an answer that has the same effect as it. Any answer we pick will always be subject to the 3rd rule, which we can still use, so this is not a useful way to evaluate answers.

With this analysis, I had (C) & (D) as answer contenders:
(C) Diagrammed: R NOT 7 (R open to go anywhere else) T in 7.
CP: T NOT IN 7 (this means T is in 1 because of rule 3) R in 7
This forces T to be in 1 or 7.

As before, you're evaluating the answer by whether it puts T in 1 or 7. That's not the rule we're trying to replace. For a specific problem with this answer, note that when R is not 7, T certainly doesn't have to be 7. T could be 1, with R anywhere else! Answer choice (C) forces T to be 7 anytime R isn't, which isn't true.

(D) T IN 7 R NOT IN 7
CP: R IN 7 T NOT IN 7 (this means T is in 1 because of rule 3)
This also forces T to be in 1 or 7.

This isn't what answer choice (D) says. It's:

T1 R7

and the contrapositive:

R7 T1

That's not even true - If R is 7, T must be 1. So this isn't even a true statement.

Did I misunderstand the meaning of rule 4? I don't understand why (C) & (D) are incorrect.

Now I've dealt with that. Moving on:

I thought (E) introduced a new condition as if R isn't in 1, R can go anywhere (didn't want to make a mistaken reversal of R's limitation). What makes (E) the correct answer choice?

Nothing about answer choice (E) prevents R from going anywhere the original conditions allow. The original conditions force R to be 1 if T is not 1. So answer choice (E) is certainly true:

T7 R1

because if T is 7, T is not 1, so R needs to be 1. That's all to the good. What if T is not 7? The rule says nothing in that case - if T is not 7, the sufficient condition of the new rule is false, so the rule "turns off" and doesn't do anything. So R is now free to go anywhere. That's as required, so answer choice (E) is correct.

Robert Carroll