#9 - Since anyone who supports the new tax plan has no

[alsakka]

This is what I got the from the stimulus:

If support new tax plan -->NOT chance of being elected

if truly understand economics --> NOT support new tax plan

conclusion:
if chance of being elected -->truly understand economics

are these conditional statements correct?
and if they are, I still don't understand how D is the right answer choice

isn't this what D is saying:
NOT support new tax plan -->NOT truly understand economics ?

[Nikki Siclunov]

Hi,

Your analysis of the conditional structure of the argument is correct. To summarize:

Premise: Support NO chance

Premise: Understand NO Support

Conclusion: Chance Understand

This conclusion is clearly flawed. If someone had a chance of being reelected, by the contrapositive of the first premise we know that they would not support the new tax law. The second premise, however, does not allow us to continue with our chain of deductions. If someone does not support the new tax law, that does not necessarily mean that they truly understand economics (this would be a Mistaken Reversal): the argument ignores the possibility that some people who satisfy the necessary condition of the second premise do not satisfy the sufficient condition. In other words, it is entirely possible that someone does not support the tax law AND also does not understand economics. This prephrase is consistent with answer choice (D).

In general, a Mistaken Reversal can be described in a number of ways. To make things simpler, consider the following example:

Everyone who goes to law school must have taken the LSAT. Jack took the LSAT. Therefore, Jack is going to law school.

Law School LSAT

LSAT (J) Law School (J)

The argument confuses a necessary condition for a sufficient condition. In other words, the author ignores the possibility that some people who take the LSAT (i.e. meet the necessary condition) do not go to law school (i.e. do not meet the sufficient condition). We can also describe the error in reasoning as an unwarranted assumption: the argument presumes without justification that everyone who takes the LSAT goes to law school.

It is imperative that you recognize the multiple ways in which a Mistaken Reversal (or Negation) can be described on the exam. Check out our discussion of this in Lesson 7 of the full-length course.

Thanks!

[willyhud]

Thank you so much for having this forum you all are really amazing.

For this problem, the premises are:
if support tax plan ---> NOT elected
if understand economics ---> NOT support tax plan
therefore;
if support tax plan ---> NOT understand economics

The conclusion is:
if elected ---> understand economics

The argument is flawed because (D) it ignores the possibility that "some people who do not support the tax plan do not truly understand economics."

I believe I'm solid on diagramming these relationships but I can't quite see how the individual stimulus pieces fit together to get the answer!

[Jon Denning]

Hey Willy - thanks for the question. Yeah, looks like you've got it right. Here's how I diagrammed the premises:

Prem 1: Support Tax Plan --> Not Elected [contrapositive: Elected --> Not Support Tax Plan]

Prem 2: Understand Econ --> Not Support Tax Plan [contrapositive: Support Tax Plan --> Not Understand Econ]

Now at this point you don't really have much in the way of absolute inferences, since the connecting term "Support Tax Plan" (or its negation) doesn't allow the arrows to point in the same direction:

(1) Not Understand Econ <-- Support Tax Plan --> Not Elected OR
(2) Elected --> Not Support Tax Plan <-- Understand Econ

Either way, you would have to mistakenly reverse one of the statements about Understand Econ/Support Tax Plan to arrive at the conclusion: Elected --> Understand Econ

More specifically, if you reversed in (2) above Not Support Tax Plan <-- Understand Econ you'd have consistent arrows from Elected to Understand and arrive at the exact conclusion given, which means that reversal is the mistake that the author has made. One way to describe that mistaken reversal is to simply state that the original end of arrow, necessary term (Not Support Tax Plan) doesn't tell you with certainty about the beginning of arrow, sufficient condition (Understand Econ), so that there could be some people who don't support the plan (necessary) and who also DON'T understand econ (negated sufficient).

Put more simply, the author assumed the reversal because he/she believes it's okay to move from necessary to sufficient, as in Not Support Tax Plan --> Understand Econ. To show the error in that, simply say that some Not Support Tax Plan do NOT Understand Econ. That's exactly what (D) does here.

Final point I'll make is that this is actually a really nice representation of how to attack a conditional statement: show that the sufficient condition may not always lead to the necessary condition, and the whole relationship falls apart. So here when you see that the author reversed a given relationship to arrive at Not Support Tax Plan --> Understand Econ, and you want to point out the mistake in that, simply show that the sufficient condition the author gives (Not Support) may not give the author's necessary condition (Understand). "Some people who don't support plan also don't understand econ" does that perfectly.

I hope that helps to clarify!

Jon

[reop6780]

This is "flaw" question, but deals with conditional reasoning.

The difficulty of analyzing CR in the stimuli arose from the expression of "only" in the 4th sentence.

According to the bible, "only" is the indicator of necessary condition, but ppl "who" is the indicator of sufficient condition as well.

Since the sentence starts as "only someone who ...," I could not tell if it is necessary or sufficient.

Is either one of them dominant? (only vs who)


Anyway, I could draw some relationship in the stimuli

New Tax elected

Economics Tax

either Economics elected

or Elected Economics

If the second conclusion is right, I can reach the correct answer D in the following way.

Elected Tax ; however negated Tax does not mean excellence in economics either since " " allows for negation for both conditions.

Answer D points out that the conclusion ignored such possibility.

Elected leads to negated tax, which result in both economics and negated economics.

Also, is there more efficient way of solving this problem based on intuition for example?

I tend to draw sth simple following lines in the stimuli but sometimes it get lost. Is establishing relations among conditions best way to solve these problems?

[Robert Carroll]

reop,

Just as "only if" indicates a necessary condition, even though it uses the word "if", which normally indicates a sufficient condition, "only someone who" indicates a necessary condition. The "only" makes the whole phrase necessary.

Therefore, the conditional in the conclusion is:

someone has a chance of being elected that person truly understands economics

It looks like you were on the right track in seeing that the conditionals in the premises create some double-not arrows:

supports the new tax plan has a chance of being elected

understands economics supports the new tax plan

Since these are double-not arrows, the only thing excluded is that the things on each side are both true. There's nothing that says they can't both be false. So, for instance, someone could fail to understand economics AND fail to support the new tax plan. The conclusion says that anyone who has a chance of being elected must truly understand economics. By the double-not arrows, we can see that someone who has a chance of being elected cannot also support the new tax plan. But if they don't support the new tax plan, do they need to understand economics? No; in the second double-not situation there, someone can fail to understand economics and fail to support the new tax plan. And that is exactly what answer choice (D) says.

Diagramming helps because, once you've made explicit what things can't go together, and why, you can easily check the possibilities that are still open, and see why the conclusion doesn't have to be true. Now, it's hard to do this if you're not sure what's the sufficient and what's the necessary condition, and this was troublesome for you in this question. That's why it's vital to practice identifying the sufficient and necessary conditions whenever there's a conditional in the stimulus. If the phrasing throws you a curve, like it did here (where it mixed keywords so you weren't sure which was sufficient and which was necessary), try to rephrase what's being said. Here, the conclusion (which was flawed!) claimed that a person who has any chance of being elected MUST truly understand economics. If you're not sure what's sufficient and what's necessary, ask yourself: if I have A, do I have to have B? If so, then B is a necessary condition and A is a sufficient condition. If not, then ask: if I have B, do I have to have A? Then A is a necessary condition and B is a sufficient condition. If neither is necessary or sufficient for the other, then they aren't directly connected. Look for chains of conditionals that might connect them.

Robert

[reop6780]

Your explanation really helped me a lot!

Thank you, Robert!

Hyunju

[BrettKobes]

How do you know to use double not arrows versus normal arrows and negate the necessary condition? anyone who supports the new tax plan --------> chance of being elected (with diagonal line through it)

[Adam Tyson]

Brett,

Any conditional relationship that has a sufficient condition that is positive and a necessary that is negative can be diagrammed with a double not arrow, which is just a handy way of saying "these two things can't both happen". So "if I go on vacation I will not get a promotion" leads to:

vacation <-I-> promotion

I might do one, I might do the other, I might do neither, but both is out the window.

Your diagram is absolutely accurate, but the use of the double not arrow can help to make it a little clearer, and it saves time on doing the contrapositive.

I hope that helped!

[BrettKobes]

Awesome, Thanks