#9 - If a mother’s first child is born before its due date

[Administrator]

Complete Question Explanation

Parallel Flaw, SN. The correct answer choice is (C)

The stimulus features conditional reasoning, which is identifiable by the use of the sufficient condition indicator “if” in the first sentence. The conditional relationship can be diagrammed as follows:

• FBP = First child born prematurely
  SBP = Second child born prematurely
  
  FBP SBP

The first clause of the second sentence indicates that the necessary condition has not occurred, as Jackie’s second child was not born before its due date:

• SBPJackie

On the basis of this information, the author concludes that it is likely that the sufficient condition did not occur, i.e. that Jackie’s first child was probably not born before its due date:

• FBPJackie

While the conclusion appears to be based on the contrapositive of the conditional relationship, there is a peculiarity in the language that reveals the flaw in the argument, and that you can use to your advantage when attacking the answer choices: the phrase “likely” appears just before the necessary condition in the first sentence, and when this event has been found not to occur, the author uses the same phrase (“likely”) to qualify the conclusion.

The entire form of the argument, then, appears as follows:

• Premise: FBP SBP (likely)
  
  Premise/Conclusion: SBPJackie FBPJackie (likely)

Many students, when examining this argument, do not realize at first that there is a flaw present. The structure appears to be that of a contrapositive, and they simply accept that the argument is sound and move on. But, the question stem clearly notes that the argument is “questionable,” so let us take a moment and see where the error occurs. As mentioned before, the use of “likely” is at the heart of the problem, and in the argument the author does not make a perfect contrapositive but rather shifts the word “likely” from the from one necessary condition to the other necessary condition (as opposed to the sufficient condition, where the “likely” should have moved during the contrapositive). Here’s how the argument would have appeared if the argument was sound:

• Premise: FBP SBP (likely)
  
  Premise/Conclusion: SBPJackie (likely) FBPJackie

Note how the “likely” should have moved from the necessary to the sufficient, but in the actual argument the author moved it from the necessary condition to the necessary condition (which was the conclusion).

Because your job is to parallel the argument, you must parallel the conclusion as well as the premises, making sure to “match” the certainty level of all subcomponents in the argument. The correct answer choice should contain a seeming-contrapositive argument form, and also have the same probabilistic language (“likely” or a similar term) modifying both the necessary condition and the conclusion. This knowledge allows you to quickly eliminate answer choices (D) and (E) from consideration, and focus your analysis of the conditional relationships in answer choices (A), (B), and (C).

Answer choice (A): Although this answer choice uses the same probabilistic language as the stimulus (“probably” is synonymous with “likely”), it is incorrect because the argument is in the form of Mistaken Negation:

• Premise: Finish Project Go to Fair (probably)
  
  Premise/Conclusion: Finish ProjectBen Go to FairBen(probably)

Note that this answer choice uses the sufficient condition indicator (“people who”) instead of “if.” This difference is inconsequential and should not be used as grounds for eliminating the answer.

Answer choice (B): Although this answer choice also uses the same probabilistic language as the stimulus, it is incorrect because the argument is in the form of Mistaken Reversal:

• Premise: Resp. Owner Good with Kids (probably)
  
  Premise/Conclusion: Good with Kids Resp. Owner (probably)

As with answer choice (A), the difference between the sufficient condition indicator used in the stimulus (“if”) and the answer choice (“all”) is irrelevant, since they both modify the same type of condition.

Answer choice (C): This is the correct answer choice. The argument is in a contrapositive form and therefore matches the logical validity of the stimulus. It also uses the identical term “likely” in the necessary condition and a synonymous term “probably” in the conclusion:

• Premise: Movie a Hit Sequel a Hit (likely)
  
  Premise/Conclusion: Sequel a HitHawkII Movie a HitHawkI (probably)

Also, note that this reasoning matches precisely the abstract nature of the argument in the stimulus: if the first occurrence in a series of events has a certain characteristic, the second occurrence in that series is likely to have the same characteristic. Therefore, if the second occurrence did not have that characteristic, it is likely that the first one did not either. You should not be concerned with the fact that the characteristic in the stimulus was a negative one (premature birth), whereas the characteristic in answer choice (C) is positive (box-office hit). Remember—the topic in Parallel Reasoning questions does not matter, as your only job is to identify an argument that has a similar pattern of reasoning.

Answer choice (D): This argument is valid, but it is not in a quasi-contrapositive form. In fact, the conclusion is a Repeat of the premise:

• Premise: Fail (likely) Invest
  
  Premise/Conclusion: FailPS (likely) InvestPS

Also note that the word “likely” here qualifies the sufficient condition of relationship, not the necessary condition as in the stimulus. Furthermore, the conclusion does not feature the same probabilistic language. A savvy test taker who notices this difference may choose not to even diagram this answer choice, and automatically eliminate it from consideration.

Answer choice (E): This answer choice is incorrect because the argumentation is in the form of Mistaken Reversal:

• Premise: SailingTai Nice Weather
  
  Premise/Conclusion: Nice Weather SailingTai (probably)

As with answer choices (A) and (B), the difference between the indicators used in the stimulus and the answer choice is irrelevant. In this case, the phrase “only if” indicates that having a nice weather is a necessary condition for sailing; the fact that the same indicator was not used in the stimulus does not matter.

What matters, is that the necessary condition in the premise does not feature the same probabilistic language we have come to expect. This difference, although minor, is sufficient to eliminate this answer from contention, the Mistaken Reversal error notwithstanding. Remember, all relevant elements of the argument must be paralleled, not just some of the elements. This can save you time, as you need not diagram every single answer choice in order to arrive at the correct answer.

[netherlands]

Hi there PS,

I just wanted to check something. In this question they used some conditional language/structure to make it seem like this was a conditional reasoning question. But they also use the term "likely" which means its not conditional because it is not absolute.

I just followed the structure and language to get to the right answer, C. But was the flaw their act of treating this relationship as a conditional one and trying to assume a contrapositive of it, which can't be valid since it's not an absolute conditional relationship.

Basically you can't assume the contrapositive of an "If then" statement if it uses the term "likely" within it.

Thank you!

[Jason Schultz]

Hi there netherlands,

Good question. You are on the right track, but the flaw goes slightly deeper. When you have a conditional statement like this, it is possible to create a legitimate contrapositive, but you must know that the two groups are the same size (or that the first group is larger). In this case, the groups are "First children born before their due date" and "Second children born before their due dates." Since they don't tell you this information, the contrapositive is not properly reasoned.

Here's an example of the bad reasoning with numbers. Imagine there are 100 premature first children but 10,000 premature second children. It is "likely" that a woman with a premature first child will also have a second, so lets just say that 99 of those 100 lead to 99 premature second bables. Since obviously a woman must have a first child in order to have a second, that means 9,900 first children were born on time and then the woman had a premature second child. So one could not possibly conclude that it is "likely" that a premature second child indicates a premature first child.

Now imagine the numbers are equal= 100 premature first children and 100 premature second children. If 51 of the premature first children are followed up by premature second children, then you can logically conclude that a premature second child means the first child was likely premature as well.

Answer choice C shares this mistaken equivalence, with just 'Hit movies' and 'Hit sequels.'

So to wrap up a long answer to a short question: It depends. It is possible to create a legitimate contrapositive to a qualified statement, but you need more information.

For a very similar example, look at question #4 in the parallel flaw section of Lesson 8, page 8-8 regarding the bicyclists in Sheldon.

[Rita]

Hi Jason,

I still don't fully understand the mistake. Could you please explain exactly when a conditional argument containing the term 'likely' can be negated, and when (as in this case) it can't?

Thanks,
Rita

[Emily Haney-Caron]

Hi Rita,

For the most part, you won't be able to create an accurate contrapositive with a conditional statement with likely such as this one. In this case, you would be able to do so only if you also knew that the second group isn't larger than the first group. You can think of the relationship here as "if x, then likely y," where x is first child is born before its due date and y is "second child born before its due date." y is the second group, x is the first group.

Make sure you check out the other example Jason pointed out, if you haven't gotten a chance to do that yet! Let me know what you think of that one when you look at it in light of Jason's post, and we can try to help you further.

[kcho10]

Hi,

I noticed that the LSAT superprep explanation also adds that for answer choice D, the premises can validly infer that 'people will not invest in Pallid Starr' but the actual conclusion of D is 'no one is likely to invest in it', so it is invalid. The only difference I see between the 2 statements is that the second statement is a weaker version of the first, which shouldn't be a problem because it is easier to prove. No matter how much I look at it, D seems valid to me. Could someone explain what the difference is between the 2 statements that makes this answer choice invalid?

[Adam Tyson]

Actually, kcho, answer D IS valid - if nobody will invest, then it is certainly true that nobody is likely to invest, right? I'm not sure where that explanation is that says D is invalid, but if it is one of PowerScore's explanations, please tell us where you found it and we will give it another look.

That's one very good reason why D is not the correct answer - it's valid, and we are looking for something that is flawed. Putting that aside, though, we can also see that it is not a parallel answer because the premise in the stimulus was about liklihood (if one thing happens, a second thing is likely), whereas the premise in this answer choice has that turned around and becomes about certainty (if one thing is likely, a second thing is certain). Since the language of that premise and the relationship it describes is opposite the language and relationship found in our stimulus, it cannot be parallel to the argument and therefore must be an incorrect answer choice.

Look for those subtle but crucial differences! Order may not matter in parallel reasoning and parallel flaw questions, but the logical relationships must be the same.

[jessicamorehead]

For this one, I saw the flaw entirely differently. At first I was tempted by the conditional language, but I knew that the word 'likely' did not constitute a conditional relationship. So, I saw the flaw more abstractly as a timing issue. The stated relationship is about the first child occurring before the second child, whereas the conclusion tries to make a deduction about the first child based on the second. Answer choice C does this too. The original movie happened before the sequel, but the conclusion tries to make a deduction about the original movie based on the sequel.

I also redid the problem focusing on conditional language and found the following: (I'm using the word "fake" because of the answer choice's use of uncertain language)

A) represents a fake MN
B) represents a fake MR
C) like the stimulus, represents a fake CP and also has the timing element of one thing occurring before the second
D) valid reasoning
E) represents a fake MR

Let me know if my logic is sound here! Thanks

[Adam Tyson]

Looks solid to me, Jessica! Nice work! I agree with your "abstract reasoning" approach, as opposed to a more formal conditional reasoning approach, especially in the presence of "likely". One could also eliminate certain answer choices simply because they didn't match that same force of language - answer E, for example, has a true conditional premise built on certainty rather than likelihood, so it's out.

Whatever tools you have to bring to bear on a task, bring them! There is usually more than one way to get to the best answer!

[jessicamorehead]

Adam,

Wonderful! I just wanted to make sure I didn't make up the "timing flaw" in my head. Thank you for always taking the time to answer my questions on the forum! Have a great weekend

Jessica