#23 - Global, Rule Substitution

[Administrator]

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=15133)

The correct answer choice is (B)

This is the infamous Rule Substitution question, a staple in the Logic Games section as of late. Considering their growing popularity, tackling such questions is no longer merely optional: it is imperative to have a workable strategy in place. Although the difficulty of this question may have been compounded by the fact that it was the final question in the section, a closer look reveals that the correct answer choice (B) is a straight restatement of the rule in question. Do not assume that the Rule Substitution question will necessarily be difficult! If you skip such questions by default, you may be robbing yourself of an easy point.

The question stem asks you to replace the fourth rule of the game, according to which if M is published in the fall, N must be published in the spring:

• MF NS
  
  Contrapositive: NF MS

Our job is to substitute that rule with a logically equivalent condition, which would have the exact same effect on the order in which the houses are shown. While the wording of the correct answer can be difficult-to-impossible to predict, the four incorrect answer choices will either present rules that were not part of the original rule set (also known as Additional Effects conditions), or else they will only partially constrain the variables in the rule being substituted (i.e. Partial Match conditions).

Since Additional Effects are easier to spot, look for answer choices that contain such conditions first. Answer choice (A), for instance, addresses the placement of L, which was never addressed in the original rule set. Answer choice (A) can be eliminated for that reason alone. Likewise, answer choice (D) contains a rule whose contrapositive contradicts the rule being replaced:

• Answer choice (D): NS MS
  
  Contrapositive: MF NF

Answer choice (D) must therefore also be eliminated.

We now need to consider the remaining three answer choices more closely:

Answer choice (B) is the correct answer choice. This rule establishes the following conditional relationship:

• NF PF

This condition is consistent with our original inference that if N is published in the fall, then so is P (see conditional chain). Answer choice (B), therefore, does not contain an Additional Effects rule.

The better question is: does answer choice (B) contain a Partial Match? It does not, because M and P cannot be assigned to the same group as each other (first rule), and so P being published in the fall is synonymous with saying that M is published in the spring. Thus, the effect of this rule is identical to that of the contrapositive of the original rule:

• NF PF MS

Answer choice (C) establishes the following conditional relationship:

• MS PF
  
  Contrapositive: PS MF

This is a partial restatement of the first rule, which clearly does not necessitate the relationship between M and N established in the fourth rule. Answer choice (C) is therefore a Partial Match condition, and is incorrect.

Answer choice (E) establishes the following conditional relationship:

• OS .....NS
  
  Contrapositive: NF OF

This rule is consistent with our original inference that if N is published in the fall, then so is O (see conditional chain). Answer choice (E), therefore, does not contain an Additional Effects rule. However, it does contain a Partial Match, as it does not force a relationship between M and N identical to that of the original rule. Nothing is stopping us, for instance, from publishing both M and N in the fall, along with K and O. Such a solution would be in violation of the original rule set, but nevertheless consistent with the rule in answer choice (E):

PT76_O15 LG Explanations_Game #3_#23_diagram 1.png

Since answer choice (E) allows for a solution prohibited by the original set of rules, it contains a Partial Match and is therefore incorrect.

[manderz]

After reading this explanation I understand why B is the right answer, however I'm still confused on these type of questions, what exactly are we looking for here? I'm just confused.

[Jeremy Press]

Hi manderz,

What you're looking for here is a rule in the answer choices that does exactly the same thing as the rule you're substituting for in the question stem.

This means the new rule must be exactly as restrictive and permissive as the original rule. The rules in the wrong answers will either (1) permit you to do something that the original rule wouldn't have permitted you to do (that's what the explanation means by "Partial Match") or (2) restrict you from doing something that the original rule wouldn't have restricted you from doing (that's what the explanation means by "Additional Effects").

Another way of looking at the question is to try to find an answer that, if you swap it for the rule in the question stem, will produce the same diagram as you had originally. Answer choice B does that because its necessary condition (P in the Fall) produces the same necessary condition as the contrapositive of the original rule (M in the Spring). So, when I swap out the rule in B for the rule in the question stem, I still get the same rule as I had originally. Rule in answer choice B = N(f) P(f) M(s) {the chain produced by answer choice B}, which has as its contrapositive the same thing as the original rule, i.e. M(f) N(s).

If you happen to be a PowerScore course student or a reader of the Logic Games Bible, there is a lengthy discussion of these questions in the Logic Games Bible, and in the Lesson 7 Supplemental area for the Full-length and full Live Online classes.

I hope this helps!

Jeremy

[Jeremy Press]

One more little note for you, manderz: here is a list of every Rule Sub question that has appeared on the test, in case you'd like to practice more of them!

https://www.powerscore.com/gamesbible/l ... /index.cfm

[michaelkennedy]

Maybe I am not fully understanding the end goal of these questions, as I am very confused about how exactly to attack problems such as these.

My thought process went as follows:

For If M (fall) --> N (spring), then you can utilize those rules to come up with a diagram that looks something like this:

Fall Spring
M N
P
K

Substitute: N(fall) --> P(fall)

Fall Spring
N M
P
K
O

In this case, with answer choice B, the orders, even despite the fact that they are swapped from fall to spring, are not the same, as if you substitute the rule, and force P to be in the fall, then you force O to be in the fall as well, per the "If k is published in the fall, O must also be published in the fall." In this case, you are fixing O when you substitute the answer choice B question for the original rule of If M (fall) --> N (spring), where as under the conditions of the original rule, O was not fixed, and able to go into either the fall or the spring.

Am I approaching these questions wrong? It seems that in this case I took an extra step when it was not necessary, while my focus should have instead been on purely the logic of the rule, without thinking about the secondary effects of the rule being changed.

[Adam Tyson]

The correct answer for these questions will have the same overall effect on the game. That means it will lead to all the same solutions, all the same answers to the questions, and could ultimately be diagrammed in exactly the same way as the original rule. That includes answers that are the contrapositive of a conditional rule, as in this case. The contrapositive would have been if N is in the Fall, M is in the Spring, and that of course forces P into the Fall per the M/P rule. So if we say N in the Fall forces P into the Fall, that also forces M into the Spring; the contrapositive would be if P is in the Spring (and M is therefore in the Fall), N is in the Spring. That's the same result!

So it's more than just the logic of the rule itself, although that's a good starting point. It also involves how that restatement of the rule impacts other rules and variables.