#23 - When people experience throbbing in their teeth or

[Administrator]

Complete Question Explanation

Parallel Flaw-SN. The correct answer choice is (D)

This is another Parallel question that contains conditional reasoning. Notice that the question stem mentions the "error of reasoning." Any time a Parallel question mentions "flawed reasoning" or an "error in reasoning" and it contains conditional reasoning, the "flaw" or "error" is most likely either a Mistaken Reversal or a Mistaken Negation. In this case, the stimulus contains a Mistaken Negation.

You can diagram the stimulus as follows: If T (throbbing) then P (serious dental problem). If P then TD (tooth decay) or GD (gum disease). These two statements combine then to say: if T → TD or GD. Then the conclusion is: T (not throbbing) → TD or GD. This is a classic mistaken negation. We simply need to diagram the answer choices to find another mistaken negation.

Answer choice (A): The reasoning in this answer choice is sound. If C (a person drinks a lot of coffee) then JN (jittery nerves). If JN → N or S (neither types of medicine). Therefore, If C → N or S. The conclusion is the second sentence here (notice the "therefore"), so be careful not to assume the conclusion is always the last sentence and let this answer choice trick you.

Answer choice (B): Again, this answer choice has logically sound reasoning. First, however, notice that the conclusion is "he is not doing so legally." This conclusion does match the conclusion in the stimulus because it has two aspects—"neither tooth decay nor gum disease." This answer is a legitimate contrapositive. It would be diagrammed as follows: if LP (legal psychiatrist)→MD and T. T→ LP.

Answer choice (C): Although this answer choice demonstrates flawed reasoning, it does not match the reasoning of the stimulus Again, notice that the conclusion here is "probably not" which is not the same as the absolute conclusion in the stimulus. If SNC (severe nasal congestion) → SI or A (sinus infection or allegery). SI→ SNC. This is not a contrapositive because only one of the "or" terms is negated and they would both have to be to make it logically sound. However, that is not really of concern because the reasoning does not match and the conclusions are entirely different (notice the "not").

Answer choice (D): This is the correct answer choice, another Mistaken Negation. If P or C (if interested in physics or chemistry) then CM (consider a career in medicine). P and C→ CM. Notice the double element of the conditional reasoning, and especially notice how the Mistaken Negation matches exactly.

Answer choice (E): Although this answer is more difficult to diagram, you can eliminate it immediately by finding the conclusion and doubling it with the stimulus. "Kim must have been trained" is different than "can be suffering from neither." Here the diagram would be: If ST (specialized training) →Oph or Opt. Kim has ST →Kim must be Oph or Opt.

[reop6780]

This is parallel type that I've been recently working on in Question Type Training book

I'm usually confident in this type but honestly this type consumes up to 2 min of my time - is this very abnormal?

Since this question was located at the end, I could not allocate more time.

Anyway, about the "negation" used in the stimuli.

In general, should the correct answer parallel how the stimuli is negated as well?
(eg conclusion and reasoning should be matched)

More specifically, can I exclude answer E based on its negation, "neither an ophthalmologists nor an optometrist" when the stimuli advances its idea, "either throbbing in the teeth or gums" ?

[Robert Carroll]

reop6780,

This type would go more quickly if you identified more quickly what the flaw in the reasoning was. In this case, just diagram the conditionals:

throbbing in teeth or gums -----> serious dental problems

serious dental problems -----> tooth decay or gum disease

The conclusion:

not(throbbing in teeth or gums) ------> not(tooth decay or gum disease)

It will be clear now that the flaw is a Mistaken Negation. Use the keywords indicating conditionals (if, when) and set those up, and it will be easy to check on the diagram what flaw is being used.

When you check the answer choices to find the same flaw, look for a conditional. Look for a conclusion that negates the sufficient condition, and thus tries to say that the negation of the necessary condition has to be true. If an argument in an answer choice is valid, then it can't be the answer, because you need a flaw! If an argument is flawed, then look for the identical flaw. Use concepts like Mistaken Negation (if present in the stimulus, of course) to identify quickly what you're looking for.

Although E is the wrong answer (it certainly doesn't use Mistaken Negation), you can't exclude it just for saying "neither...nor" rather than "either...or". The flaw here is Mistaken Negation, and any phrase can be negated, even if it differs in wording and indeed in meaning from what's used in the stimulus. What should clue you in quickly that E is not the right answer is that the NECESSARY condition is the thing being negated, and that is supposed to lead to the negation of the SUFFICIENT condition. You're looking for a Mistaken Negation, while E is giving you the contrapositive - not what you need.

In short, in Mistaken Negation, you need a premise that says "sufficient -----> necessary." Each of those conditions COULD be a compound phrase. The conclusion will say "negation of sufficient, therefore negation of necessary", and this will be wrong.

Robert

[reop6780]

Hi, Robert. Your reply helped me a lot and reduced much confusion to me.

I should focus more on identifying flaw in the stimuli !

[jessicamorehead]

Question regarding conditional diagraming.

When the stimulus says "if neither A nor B then C"

is that diagrammed as

NOT A
AND --> C
NOT B

or is it diagrammed as

NOT A
OR --> C
NOT B


basically, does "neither/nor" have an "and" or an "or" between the two options?

[AthenaDalton]

Hi Jessica,

Neither/nor are diagrammed with an "and" between them. Here's how:

Neither Sabina's teeth nor her gums are throbbing, so she is not suffering from a serious dental problem

If NOT experiencing throbbing in teeth AND NOT experiencing throbbing in gums NOT Serious dental problem

Best of luck with the test next week!

Athena

[dandelionsroar]

Hi,

Your explanation for e had me wondering, could an answer choice be correct if it parallels the structure of the question stem except for that it uses the contrapositive instead in the conclusion? Would that mean the conclusion is not parallel or since the contrapositive is saying the same thing in an alternative way in terms of paralleling it is logical equivalent?

Thanks!

[Adam Tyson]

A contrapositive of the structure in the stimulus CAN be a valid answer in Parallel Reasoning, dandelionsroar, but it almost never is. The only time I might expect the right answer to contrapose the structure is when the stimulus uses one of the special necessary condition indicators (unless, except, until, without), because while we at Powerscore treat those as necessary indicators, many others treat them as a form of sufficient indicator equal to the phrase "if not." Since the stimulus could therefore be diagrammed in either direction, with the two options being contrapositives of each other, I would not be surprised to find an answer choice that is the contrapositive of what I was looking for.

Simple example: the stimulus says "X unless Y, and Y did not occur, so X must have occurred."

Powerscore method: X Y; Y, therefore X

"If not" method: Y X; Y, therefore X

Parallel answer: "if C does not occur, D must occur, and C did not occur, so D must occur."

Using our method, this answer looks like a restatement form instead of the contrapositive we expected, but using the other method it is a perfect match. For this reason, we can confidently select this answer despite it not being what we expected it to look like.

Most of the time, though, you are going to find an answer that is a perfect match, not a logically equivalent contrapositive. If you have to choose between a contrapositive and a perfect match, go with the perfect match. If a contrapositive is the best we have to work with, then select it and don't fret!

[Chi567]

I got the answer right but I saw this as a false dilemma flaw in the reasoning type question, where they are only presented with two options. Answer choice D was the most similar to that flaw in reasoning. Can you approach the question from that angle?

[Rachael Wilkenfeld]

Hi Chi,

This isn't quite a false dilemma. A false dilemma requires that there be some additional possibility not considered by the argument. There is no reason to think that tooth decay and gum disease aren't the only reasons for serious dental problems. In the answer choice, the argument doesn't even limit itself to the categories of physics and chemistry. It only says that if you have those interests, then you should consider a career in medicine. It doesn't say only those who have those interest should have a career in medicine.

False dilemmas look a bit different. They typically try (unreasonably) to split the possibilities into two groups. "Either you are with us or against us." Well, maybe, or maybe you just don't care enough to be either. "Either it's cold or it's hot." It could be somewhere in the middle. "You need to let me stay up all night reading, or you don't think reading is important." We don't have any of this type of improper limitation here.

Hope that helps!