Q22 - Most people who shop for groceries

[mrudula_2005]

Hi,

So what exactly is the flaw in this stimulus?

Can you talk me through this kind of flaw because i've seen it several times throughout my prep and can't seem to articulate it or explain it to myself clearly even though I have an intuitive grasp of what it is:

Is it just that the author is inferring from the fact that MOST people of a general population do something that MOST people in a specific population do something and this is flawed because it very well could be that those shoppers in Hallstown who shop for groceries no more than 3 times a month could all be or could be for the most part made up of the MINORITY of the group of those who shop for groceries no more than 3 times a month in that they do NOT buy prepared frozen dinners regularly so the conclusion that "therefore in hallstown most people buy prepared frozen dinners regularly" is totally unjustified? or is there another flaw as well...that just because most people in the town shop for groceries, doesn't mean definitively that most people in that town engage in behavior that characterizes most of that population - just because most ppl inhabit a town and mostly do one thing doesn't mean that most of the ppl in that town therefore do that thing - because all of them could be in the minority or at least a significant part could be in a minority and not prepare frozen dinners regularly. ah. i just want a way to simply and succinctly articulate this!



I am probably not being clear, but basically is part of the flaw that the author is overlooking the fact that of that group in the first line "people who shop for groceries no more than 3 times a month", while MOST prepare frozen dinners regularly, it could very well be that everyone in hallstown who shops for groceries no more than 3 times a month fall into the minority of the general population in not preparing frozen dinners regularly?

thanks for dealing with this!!!!!

[aileenann]

Hi there,

I completely agree with your articulation of the flaw here, especially the way you phrased it at first. Just because the people of Hallstown fall into a larger group most of which does something else, doesn't meant they are in the majority of that group's second habit. The argument is assuming they are and/or assuming that people in Hallstown have the same sort of demographics/habits as the generally representative group of people who shop for groceries no more than 3 times per month.

Another way of thinking about it is this. Just because a group belongs to set A for having one practice/characteristics, doesn't mean they have all the practices/characteristics of A so long as those characteristics are not universal. Once you are down to less than 100% coverage there is no way to prove/assure that any group you pull out of your larger group will be fully representative/in the majority.

I am not sure that is a clearer way of explaining than your own, but I thought letting you see someone else also try to put it into words would show you that you are right on track.

Hope this helps. Don't hesitate to follow up if you have your own thoughts or additional questions about this you'd like to share!

[funner567]

Hi,

first post here and absolutely loving the back and forth explanations on this site...amazing.

Now

In my understanding this seems like a Whole --> Part fallacy. Am i correct?

I dont see why "B" doesn't constitute this fallacy while "D" does, they seem very similar in my opinion

[ManhattanPrepLSAT1]

Great question! Actually I wouldn't describe this as a whole to part fallacy, though that flaw does appear regularly on the LSAT.

That flaw would sound more like, "The student who sold the most raffle tickets at Middleton School was in Mr. Matthews class. Therefore, Mr. Matthews class must have sold more tickets than any other class at Middleton School."

In this question, we have quantified logic. Frequently we use conditional statements to understand a chain of reasoning. We sometimes also use quantified statements to help see the underlying logic as well.

So for example, "if all dogs are pets, and some pets have feathers, does it follow that some dogs have feathers?" No, of course not.

But what about, "If all dogs are pets, and some dogs have long tails, does it follow that some pets have long tails?" Yep, that has to be true.

It's easier to see the logic above, because you have a reference. But if I take away your reference by discussing something completely arbitrary - say how often people shop for groceries in Hallstown - it gets much more difficult.

Think of this one as saying that. "most dogs are pets, most pets live indoors, therefore most dogs live indoors." This could be true, but doesn't have to be. This reasoning is paralleled in answer choice (D).

(A) has two independent reasons for arriving at a conclusion. The stimulus uses the premises in conjunction.
(B) is a valid argument. It's very much like the example above about dogs with long tails!
(C) doesn't match the reasoning. This has two premises that represent conditional relationships and that begin with the same sufficient condition (trigger). The stimulus has two "most" statements that attempt to link using the transitive property.
(E) is another valid argument. It links a "most" statement with a conditional statement in a permitted way.

Does that answer your question about the parts to whole fallacy here?

[funner567]

well if i dont understand it after that, then i must be in trouble. Thanks for the explanation definitely clears it up!

[LSAT-Chang]

So for example, "if all dogs are pets, and some pets have feathers, does it follow that some dogs have feathers?" No, of course not.

Hey Matt! This might be a really stupid question but for some very very weird reason, when I use symbols to represent that statement above, I tend to infer that.. That is so weird because I thought I had a solid understanding with some/most statements. So like, if we have "some As are Bs and some As are Cs" we cannot infer any overlap between B and C. But with that statement, I get:

All As are Bs, and some Bs are Cs, so some As are Cs. I tried using a venn diagram and I see how this doesnt have to be true, but I was just confused as to WHEN we can infer overlaps between 2 variables when we have 2 statements. Like we can infer an overlap between B and C if we had most As are Bs and most As are Cs since we HAVE to have at least ONE B that is a C, but your dog statement also has "All + Some" so can we not infer anything? What if we had All As are Bs and Most Bs are Cs? Can we infer some As are Cs??? I think I have the basics but get struggled when I see more than one some/most statement combined to get a conclusion (like this question -- i knew something was wrong but couldnt figure it out).

[timmydoeslsat]

This is a great post changsoyeon as this is very important.

If Dog ---> Pet some Feathers

We cannot infer that some dogs have feathers. From this conditional relationship, it COULD be the case, but the LSAT always tests us on what MUST be the case, or what we can infer.

When you have the SOME on the right hand side of an arrow, you cannot infer that sufficient condition has in common with its necessary condition that some statement.

For example:

D ---> P some F

Cannot conclude D some F.

However:

F some P--->D

You can conclude that F some D

Let me show you what I do in these situations.

When you have a straight up conditional statement, like A--->B, but then have a situation like A some C, do this

Set up your conditional A--->B

Then flip the some statement, which is perfectly valid of course, and put that C to the left of A, so that it flows nice in a visual sense.

C some A--->B

We know that C some B, or B some C, of course.

Same issue with most.

C most A--->B

We know that C most B. And we can flip that to say that B some C. When you flip most statements, it turns into a some.

You dig?

[LSAT-Chang]

This is a great post changsoyeon as this is very important.

If Dog ---> Pet some Feathers

Would this be the same as "Dog (all) --> Pets (some) --> Feathers" (I have 2 arrows whereas you have one)

We cannot infer that some dogs have feathers. From this conditional relationship, it COULD be the case, but the LSAT always tests us on what MUST be the case, or what we can infer.

When you have the SOME on the right hand side of an arrow, you cannot infer that sufficient condition has in common with its necessary condition that some statement.

I tend to write it the way I have it above with 2 arrows, because I normally link the statements, but am not used to just writing "Pets some Feathers" but more like "Pets (some) --> Feathers" and if I have it written the way I have it written, the SOME statement is in the middle of the arrow.. Or are you saying if the SOME statement is just on the right side of the ALL statement then I cannot infer that suff condition has in common with its nec condition from that some statement? I hope I'm not confusing you..

For example:

D ---> P some F

Cannot conclude D some F.

However:

F some P--->D

You can conclude that F some D

Let me show you what I do in these situations.

When you have a straight up conditional statement, like A--->B, but then have a situation like A some C, do this

Set up your conditional A--->B

Then flip the some statement, which is perfectly valid of course, and put that C to the left of A, so that it flows nice in a visual sense.

C some A--->B

We know that C some B, or B some C, of course.

Same issue with most.

C most A--->B

We know that C most B. And we can flip that to say that B some C. When you flip most statements, it turns into a some.

Great point!! But does it work if I don't flip the statement? If I have the same A ---> B and some A ---> C, Could I say:

A ---> B

and just link it this way: A some C ---> B

or can I not link something in the middle of a set conditional? Do you see what I did? Am I only allowed to link it toward the end? So like what you gave:

C some A ---> B

You dig?

[timmydoeslsat]

I would strongly advise you to drop the arrows with the some statements you write. It will not be a big deal.

A some B

If you place an arrow in that statement, you should place two arrows with that statement because of the fact that if some A's are B's, then you know the some B's are A's.

A some B = B some A

I will repeat my practice in greater detail with your concerns in mind as I explain it.

I will be listing statements that we will diagram.

If A, then B.

A ---> B

Some A's are C's

As I understand it, you have been doing this: A (some) ---> C

That is a totally inefficient way of doing this, and also dangerously confusing.

Lets watch what happens when we drop the arrow.

A some C

We can easily see that a switch of variables in this statement is valid. The idea of an arrow simply distracting in quantifying statements such as some or most.

Let us try to combine the two statements. I will first show you a mistake of trying to combine the two statements.

Our two statements are:

A ---> B

A some C

A mistake would this:

A some C ---> B

This statement above appears to show that every C is a B. That when in fact you have C, you must have B, which we know is not the case of the two statements we have been given.

Flip the some statement to show clearly that every A is a B.

C some A---> B

When some or most statements come BEFORE an all statement, then we know that the variable included in the some statement will share something with what is on the other side of that all statement.


Using the example above:

C some A---> B


We know that some A's are C's and vice versa of course.

AAAAAAA
CC

That is a hypothetical situation given above. We know that every A is a B.

So....

AAAAAAA
CC
BBBBBBBB

It will always be the case that some C's are B's. This is because of the fact that every single A is a B. And we know for a fact that some C's are A's.

However, when the some or most statement is on the right hand side of an all statement, we do not know anything FOR SURE.

Hypothetical situation:

A ---> B some C

We know that every A is a B. And we know that some B's are C's.

However, do we know whether some C's are A's? NO!!!

Here is why.

AAAAAAAAA
BBBBBBBBBBBBBBBBBBBB
----------------CCCCC

[LSAT-Chang]

Aha! I see it now. I think I was confusing myself by using the arrows for some/most statements -- but looking at your explanation above, I can clearly see how NOT having the arrows makes it so much more simpler in that I know some/most statements can go BOTH ways. So next time, if I have a statement that says:

All boys wear green hats. Some students who wear green hats wear glasses.

Then I would diagram it as:

boys --> green hats SOME glasses

And if I had:

All boys wear green hats. Some boys who wear green hats wear glasses.

Then I would have:

glasses SOME boys --> green hats

I can infer from this statement that some people who wear glasses wear green hats, but cannot infer anything from the first statement (boys --> green hats SOME glasses) whether or not some boys wear glasses.

Thanks a bunch!!!!

[timmydoeslsat]

You are correct on everything you said. Good job.

[ban2110]

Hallo,
I'm still a bit confused over the flaw in this argument. First, although I was able to match the flaw in the stimulus, I'm still having a hard time figuring out exactly why the stimulus is flawed. I diagrammed the stimulus as such:

SG most PFD
SG(hallstown) most PFD(hallstown)

The sufficient condition was met for hallstown so then doesn't the necessary automatically trigger? From your post, I get the feeling that the flaw is perhaps not conditional but "contextual" maybe? I'm not quite sure how to describe it. Is the flaw because the stimulus is trying to apply a conditional statement for a general population to a smaller population without justification? If the stimulus said: "Hallstown shoppers are generally representative of average grocery shoppers" would the stimulus no longer be flawed?

I hope my post isn't too confusing! Thank you for all the help!!

[WaltGrace1983]

Hallo,
SG most PFD
SG(hallstown) most PFD(hallstown)

The sufficient condition was met for hallstown so then doesn't the necessary automatically trigger? From your post, I get the feeling that the flaw is perhaps not conditional but "contextual" maybe? I'm not quite sure how to describe it. Is the flaw because the stimulus is trying to apply a conditional statement for a general population to a smaller population without justification? If the stimulus said: "Hallstown shoppers are generally representative of average grocery shoppers" would the stimulus no longer be flawed?

I hope my post isn't too confusing! Thank you for all the help!!

I'll try and see if I can explain it.

Most who shop for groceries → Buy frozen dinners

Here is the first statement. We know that most people in the general population who shop for groceries also buy frozen dinners.

In Hallstown, most people shop for groceries ⊢ Most people in Hallstown buy frozen dinners

This is the real meat of the argument, the premise and conclusion. As you can see, our first statement about the general population gives us a maxim: most people who shop for groceries buy frozen dinners. This argument then tries to infer something about most people in Hallstown.

The first problem is that we have no idea if the "most people" in the general population applies to the "most people" in Hallstown! Let's say we have 1 million people who shop for groceries (no more than 3 times a month). From our stimulus, we know that MOST of these people (of the 1 million) buy frozen dinners.

Therefore, we have the frozen dinner buying team, consisting of at least 500,001+ people, and the NON frozen dinner buying team, consisting of at most 499,999 people. However, how do we know where the people in Hallstown fall? What if the people in Hallstown, though certainly buying groceries no more than three times a month, are amongst the NON frozen dinner buying team? That is the flaw!

So you say that the sufficient condition is triggered. Well, not exactly. Unless we know that Hallstown people fall within the "most" sufficient condition, we don't know anything! Now if the sufficient condition of the original premise was "All people who shop for groceries...buy frozen dinners," then we could infer that, in Hallstown, the most people who shop for groceries no more than three times a month do actually buy frozen dinners. Why did I italicize that statement? Well, there is another flaw that we have all neglected.

The argument goes from talking about the most people who shop for groceries to "most people in Hallstown." This is yet another flaw because we don't know what percentage that the people who shop for groceries in Hallstown actually consist of. What if only 5 of the 100,000 residents of Hallstown shop for groceries? Could we say, from the information provided, that MOST people in hallstown buy frozen dinners? Nope.

[KayM793]

But still, I guess my main issue with D is that I can't find its conclusion. What is the conclusion of "It is clear that most people in Highland County drive sedans and most people in Highland County commute to work?" Aren't there just two parallel clauses??