#11 - Secondary school students achieve broad mastery

[Zarie Blackburn]

We recently received the following question from a student. An instructor will respond below. Thanks!

Hi. I know this is an older post but I wanted to ask a follow up question somewhat related to PT #71 Section 3 Question 11.
If a question asks you to chose the assumption that allows for the conclusion to be properly drawn- does that mean answers containing "even if" will never be correct for this question type, since "even if" statements do not affect the conditional reasoning?

This question was originally posted on the LSAT Blog here: https://blog.powerscore.com/lsat/how-to ... /#comments

[Jeremy Press]

Hi!

Great question, and an important point you're raising. I'd encourage you to review again the blog post linked above, in particular the portion of that post that talks about the effect of an "even if" clause within a larger conditional statement. It says, in summary, "How does th[e] 'even if/ clause affect the conditional rule []? The answer, oddly enough, is that it doesn’t really affect it at all. This clause is simply stating that the conditional rule above holds true regardless of whether the ["even if" clause holds true]."

In this particular question, using the above insights, what we can do with the "even if" clause of answer choice B is disregard it. Now that, by itself, doesn't mean the answer choice is necessarily or automatically wrong. It just means that portion of answer choice B is extraneous. (Remember, extraneous information doesn't destroy an answer choice in a Justify question). Once we ignore that extraneous "even if" clause, we still have to look at the remaining conditional statement, which is, "[Secondary school students] will not achieve broad mastery of the curriculum if they do not devote significant efforts to their studies." And we have to ask whether that remaining conditional statement justifies the conclusion. If it did, it would be the correct answer! But it doesn't. And that's because the conclusion of the argument relies on adding some additional information to the contrapositive of the first sentence of the stimulus (the premise). But what answer choice B gives us is merely the Mistaken Negation of (a portion of) the first sentence of the stimulus. A Mistaken Negation will not justify a contrapositive (or, in this case, a souped-up contrapositive).

I hope this helps!

Jeremy

[LawNat75]

hello thanks so much for all of your helpful explanations!!

I understand that the contrapositive is


BM--> LS or SE

and that they arbitrarily pick LS so we have to connect SE

my first question is where the third option of both comes from

my second question is about this line "What makes this question particularly tricky, however, is that the author’s explicit statement that the students are not being taught with methods appropriate to their learning styles (TMA), does not rule out the possibility that they also fail to devote significant effort to their studies (DSE). Because the options are not mutually exclusive, explicitly identifying one option does not inherently preclude the other option from being the case."

and then just where the answer comes from there


thanks so much for your help again

[Jeff Wren]

Hi LawNat,

First, just to be clear, the contrapositive would be:

Not BM -> Not LS or Not SE

(We would usually represent the negative terms with slashes rather than writing "Not.")

In logic, and on the LSAT, the word "or" is used a bit differently than we use it in everyday life. In everyday life, there is often an implied "but not both" to the statement. For example, if I say that I will either go golfing or go to the movies, you probably think it's one or the other, but not both.

On the LSAT, the word "or" basically means "at least one" and it could be both. If a statement on the LSAT says "Either A or B must happen," that means it could be just A, just B, or both A and B.

As for your second question, that statement is basically addressing the fact that these necessary terms (of the contrapositive) are not mutually exclusive, so it's possible that the students were not taught the appropriate methods for their learning styles and they also did not devote significant efforts to their studies. There are certain words that are mutually exclusive by definition, so the possibility of both happening is ruled out by common sense. For example, since "hot" and "cold" are opposites, they are mutually exclusive. If I say, "it is either hot or cold," it can't actually be both at the same time (even though the word "or" normally allows both possibilities).

What I'd recommend focusing on is what we need to prove the conclusion. As you pointed out, the author arbitrarily picks "not LS." What we need to do is get from "Not LS or Not SE " to "definitely Not LS." The most straightforward way of doing this would be if an answer ruled out "Not SE" by stating that the students did in fact devote significant efforts to their studies. If this appeared as an answer, we'd be done.

Unfortunately, to make this question more difficult, the test makers did something a bit tricky, which is to give us a conditional answer that links LS -> SE. If you take the contrapositive of this answer (Answer A), you get

Not SE -> Not LS

Then if you add this into the original contrastive of our premise, you get:

Not BM -> Not LS or (Not SE -> Not LS)

Now, either option ends up with Not LS, so we can properly conclude:

Not BM -> Not LS

which makes this argument valid.

[lounalola]

I am very confused as to why A is correct. Is A not disputing the premises of the argument? The premises of the argument says that if both conditions occur then the result will be achieved. I understand that the conclusion draws an incomplete contrapositive, but A does not even complete the contrapositive so to speak, it just changes the relationship presented in the stimulus between the two sufficient conditions. Can someone help me see this question differently?

[Amber Thomas]

Hi Lounalola!

Let's start by diagramming our relationships, using a tilde (~) to indicate negation:

Premise: Taught With Appropriate Methods + Devote Significant Effort --> Achieve Broad Mastery
Conclusion: ~Broad Mastery --> ~Taught With Appropriate Methods

As we can see, this conclusion is not a properly drawn contrapositive. An accurate contrapositive to our premise would look like:
~Broad Mastery --> ~Taught with Appropriate Methods OR ~Devote Significant Effort

We need to include the second of the necessary conditions in our contrapositive to make it accurate. Therefore, if a student is not taught with appropriate methods, or they do not devote significant effort to their studies, or both, they will not achieve broad mastery of their curriculum.

Answer choice A allows us to do this, as it states that as long as a student is taught with appropriate methods, that automatically means that they will devote significant effort to their studies. This ties effectively ties in our second necessary condition.

I hope this helps!