#25 - Interior decorator: All coffeehouses and restaurants

[Administrator]

Complete Question Explanation

Must Be True—FL. The correct answer choice is (D)

Your task in this Must Be True question is to select the answer choice that contains either a restatement of one of the facts in the stimulus, or an inference permissible from a combination of those facts. The facts presented are:

Fact: all coffeehouses and restaurants are public places

• coffeehouse public place
  
  restaurant public place

Fact: most well-designed public places feature artwork

• well-designedpublic place feature artwork

Fact: if a public place is uncomfortable it is not well-designed

• public placecomfortable well-designedpublic place

Fact: if a public place is comfortable, then it has a spacious interior

• public placecomfortable spacious interior

Given that this Must Be True question contains formal logic and the related conditional reasoning, your prephrase should focus on that those relationships. Specifically, by incorporating a contrapositive, you can combine some of the statements within the stimulus to derive an additive inference. Taking the contrapositive of the statement:

• public placecomfortable well-designedpublic place
  produces: well-designedpublic place public placecomfortable

which you can connect with the statement about spacious interiors:

• well-designed public place public place comfortable spacious interior

Thus, your prephrase is that a well-designed public place will have a spacious interior. The incorrect answers will likely present mistaken conditional inferences, in addition to the normal incorrect answer choices in Must Be True questions.

Answer choice (A): This choice presents the mistaken reversal of the last fact.

Answer choice (B): This choice presents an improper reversal of the formal logic contained in the second sentence of the stimulus.

Answer choice (C): Since the stimulus has not established that coffeehouses are well-designed public spaces, this application of the formal logical from the second sentence is not supported.

Answer choice (D): This is the correct answer choice. This choice presents the inference described above in the prephrase, that any well-designed coffeehouse or restaurant has a spacious interior.

Answer choice (E): This choice is combination of the mistaken reversals of the last two facts in the stimulus.

[LilyRose]

I know that formal logic is not a big part of the test, but this particular question gave me so many problems that I'd still like to follow up with it if. I tried to diagram as follows:

CH + R PP
WD PP FA
PP U (NOT) WD PP
C PP SI

Maybe it's because the term 'public place' is used so many times, on both sides of arrows, and usually with a qualifier (Well-designed; comfortable; etc) but I really struggled to string any of these together. I got this far (this is just the first two sentences/diagrams):

CH + R PP FA
But then I realized that might not even be right, because 'public place' as the necessary in one condition isn't the same as 'well-designed public place' as sufficient in the next. (*I know that formal logic is not sufficient and necessary - I just meant the root of the arrow vs the head of the arrow.)

So, I am fairly confident in my original translation of the stimulus to diagrams, but when it comes to linking them together (and thus finding the correct answer), I'm completely lost. Can I get some guidance please?

[Robert Carroll]

Lily,

Let's go through the diagrams one by one.

C PP

R PP

I split this up because combining the two terms with an "and" reflects the erroneous interpretation that the statement is saying something like "Places that are both coffeehouses and restaurants are public places." If something was both, of course it would be a public place according to this sentence, but the diagram combining the terms is not exactly what the stimulus says, and we want to stick to the statement as given.

PP + WD FA

This is fine. As you noticed, because not all PP need to be WD, we cannot chain together this and the previous statements.

PP + C WD

PP + C SI

We need to realize that "uncomfortable" is the negation of "comfortable" in order to make connections, if any exist, so my diagrams reflect that fact. Otherwise, these seemed fine (I know a PP that is C is a PP, so saying "WD + PP", which is already equivalent to "WD or PP", reduces to "WD").

I can see a possible chain with the last two statements, which are conditionals. In order to chain, I first need to take a contrapositive. So:

WD PP or C

Assuming something is a public place, I can say:

WD C SI

So, any public place that is well designed must have a spacious interior. I know C and R are public places, so I can say that any well-designed such place has a spacious interior, as answer choice (D) says.

Robert Carroll

[LilyRose]

Thank you so much - this brings a lot of clarity!

[jiyounglee]

How about C?

Coffeehouse (PP) + WD feature artwork?

[jiyounglee]

Is it because most well designed public place could exclude well designed coffeehouse?

For example,

most well designed public place that feature artwork could be well designed restaurants or any other places that most coffeehouses that are well designed does not necessarily have to feature artwork?

In case for

A B

B + C D

How do you connect those two conditions?
Is there a way for additive or inherent inference to be made with two conditions above via formal logic?

[Emily Haney-Caron]

Hi jiyounglee,

You are correct about why C is wrong; great job sticking with the question until you were able to reason through it yourself!

[setheli]

Hello,

Based on your contrapositive of “If a public place is uncomfortable it is not well designed”, it looks like you equate “Not uncomfortable” with “Comfortable.” But can’t “Not comfortable” be “neutral– neither comfortable nor uncomfortable”? In this case, then D would not necessarily be true.

None of the other answers must be true, and D seems like the best answer. That being said, I was hoping you could clarify the above point.

Thanks!

[Luke Haqq]

Hi setheli,

Yes, you're right--the right answer on this question is arrived at by taking comfortable/uncomfortable to be logical opposites of one another--so, they occupy the entire conceptual space. How one does this depends on what one represents with the variables. For example, "But if a public place is uncomfortable it is not well designed" could be diagramed as:

C WD

Contrapositive: WD C

"Not comfortable" and "uncomfortable" are thus interchangeable. We can add the last line--"all comfortable public places have spacious interiors" (C SI) to the contrapositive, making (D) the right answer:

WD C SI

[harvoolio]

I had very little time left when I got to #25 and did not have time to diagram it. If someone has say 1 minute left would you approach the question looking for definitive statements (all or none) that connect to other statements first. So:

1st sentence - coffeehouses and restaurants are only mentioned once skip it.
2nd sentence - most has trouble linking skipping it.
3rd sentence - comfortable used in two places.

~comfortable → ~well designed
comfortable → spacious interiors

well designed → comfortable → spacious interiors.

Scan the answers for a choice that says something that is well-designed has spacious interiors. (D) is the answer and (E) reverses it.

Thanks.