#23 - Every brick house on River Street has a front yard.

[Administrator]

Complete Question Explanation

Flaw in the Reasoning-FL. The correct answer choice is (D)

This question has a few interesting aspects. First of all, it employs formal logic, which must be
properly understood in order to identify the flaw. Second, all five answers share a common template,
beginning with, “By that line of reasoning, we could conclude that...”. Also, all five answers have
similar terms (including politician, legislator, and public servant). Finally, the five answers are
presented in inverted logical order, with the conclusions at the beginning. For these reasons, this is
potentially the most difficult and time-consuming question in this section.

The stimulus employs the following logic:

• Premise: BH FY
  
  Premise: FY 2S
  
  Conclusion (mistaken additive inference): BH 2S.

The flaw is that an additive inference through the common term “front yard” cannot be correctly
drawn here. Although “front yard” is a necessary condition for “brick house” and also an indicator
that the majority of house with front yards will have two stories, we cannot reach a proper
conclusion about the relationship between “brick house” and “two stories.” In fact, these premises
are consistent with the conclusions that no brick house has two stories, that all brick houses have two
stories, and that most brick houses have two stories. The correct answer will have premises which are
open to a similar range of conclusions.

Answer choice (A): This answer can be diagrammed as follows:

• Premise: L P
  
  Premise: L RO
  
  Conclusion: P RO

Here, the necessary condition (P) is not found in both premises and cannot be used to reach the same
flawed conclusion in the stimulus. The conclusion is simply unsupported, rather than a mistaken
additive inference.

Answer choice (B): This answer can be diagrammed as follows:

• Premise: L RO
  
  Premise: PRO PS
  
  Conclusion: PS L

There are at least two differences between this argument and the reasoning in the stimulus. First,
there is again no common term between the premises. “Politicians who have run for office” is a
subset of “run for office”, and cannot be used to draw additive inferences, even incorrect inferences.

Second, the direction of the conclusion is reversed relative to the stimulus. A more similar
conclusion would be “L PS,” rather than “PS L.”

Answer choice (C): This answer can be diagrammed as follows:

• Premise: L PS
  
  Premise: PS L
  
  Conclusion: PS RO

There are several issues with this answer. First, “some are not” and “not every” do not have the same
logical features as “most” (although it should be noted that “most are not” is logically equivalent to
“most”). Also, this conclusion contains “run for office,” which is not found in either of the premises,
while the conclusion in the stimulus only contained elements previously mentioned in the premises.
Note, however, that negating “legislator” and “run for office” in this answer choice does not make it
logically differ from the stimulus.

Answer choice (D): This is the correct answer choice. This answer can be diagrammed as follows:

• Premise: PS RO
  
  Premise: L PS
  
  Conclusion: L RO

In the answer choice, the common term is “public servant”, which is functionally equivalent to “front
yard.” This answer also incorrectly uses the common term to draw an unsupported inference about
the relationship between “legislator” and “never run for office.” Also notice that the order of the
premises is different in this answer, although this has no impact on the reasoning. Finally, since
“never run for office” has the same form in both the premise and the conclusion, it is logically
equivalent to “two stories” in the stimulus. Thus, this is the most appropriate analogy to demonstrate
that the stimulus is flawed.

Answer choice (E): This answer can be diagrammed as follows:

• Premise: PS RO
  
  Premise: L RO
  
  Conclusion: L PS

This reasoning does not contain any conditional claim like “Every brick house has a front yard.”
Also, there are four conditions in these premises (“run for office” and “never run for office” are
different conditions) as compared to only three conditions in the stimulus. Finally, this argument
does not attempt to draw an additive inference from its premises.

[netherlands]

I initially skipped this one thinking it would be time consuming, then came back later and answered it correctly although I couldn't understand why the formal logic was flawed.

So even though I could still identify the pattern, I'd like to understand the formal logic behind it.

Basically ALL Brick Houses have Front Yards and Most houses with Front Yards are 2 Stories. Is the correct interpretation of this that - there can be no relationship inferred between Brick Houses and 2 Stories, because in the formal logic rules you've given in the LR bible, ( the "train" concept) you get the "one-way" ticket on the all - but afterwards can only continue moving on another ALL, a DOUBLE or DOUBLE NOT arrow?

[Lucas Moreau]

Think of it as a function of numbers. The disconnect is because you don't know how many brick houses there are on River Street versus how many total houses there are on River Street with a front yard, and you also don't know how the "most" is distributed. Imagine the following numbers:

100 houses total on River Street with a front yard
20 of them are made of brick
80 of them are made of wood

80% of the houses (a reasonable definition of "most") on River Street with a front yard have two stories.
80 wood houses on River Street with a front yard have two stories.
20 brick houses on River Street with a front yard do not have two stories.

The point is, that "most" of the objects in a group have a certain characteristic does not necessarily imply an even distribution of that characteristic through every sub-set of that group, as demonstrated with that and with choice D.

[netherlands]

Hi there,

I can generally understand the idea, just because A shares a characteristic with, B and B shares a characteristic with C, doesn't guarantee that A will share the characteristic with C. Additionally, it's unlikely, like you said, that the characteristic will distribute evenly throughout the entire chain, which is actually a really helpful tip to always try and remember (unless maybe, we're looking at a chain of several ALLS, right? Even in this case, If all Brick Houses have Front Yards, and all houses with Front Yards are 2 Stories, then we could say that all Brick Houses are 2 Stories, right?)

But, can we not use the PS formal logic method from the bibles to understand this question? It seems like a more accurate way for me since sometimes I get worried I may be making an incorrect inference and like to use the PS method to check my inferences.

[Nikki Siclunov]

Here's how we'd diagram the formal logic for this question:

Premises: Brick house Front Yard Two Stories

Conclusion: Brick house Two Stories

The conclusion is flawed, because you need to start making inferences from the weakest link in your chain (which is the "most" link). However, the direction of the arrow does not allow you to go backwards. You can "downgrade" most into "some" (which is a bi-directional connection) and infer that some two-story houses have front yards. Nevertheless, that does not mean that some of them are brick houses, because the conditional relationship between "Brick house" and "Front yard" cannot be reversed.

There is, essentially, no additive inference you can draw from the chain above.

You can learn more about our formal logic method by going to the OSC/Lesson 8 Supplemental Resources. There is a virtual module on the topic and a fairly extensive .pdf file.

Thanks!

[Basia W]

Good evening,

I was wondering if someone could help me diagram this question out. I recognize "every" as a sufficient indicator but was not sure what "most" represented.

On a sidenote, I noticed that multiple SN questions use "since"- is this usually indicative of a necessary or sufficient indicator?

thank you for your time,

Best,

Basia

[David Boyle]

Good evening,

I was wondering if someone could help me diagram this question out. I recognize "every" as a sufficient indicator but was not sure what "most" represented.

On a sidenote, I noticed that multiple SN questions use "since"- is this usually indicative of a necessary or sufficient indicator?

thank you for your time,

Best,

Basia

Hello Basia,

"Since" is more of a premise or causal thing.
"Most" is not a sufficient indicator. Please look at the Formal Logic module in your student online material.

bh fy

h(fy) 2s

bh 2s

Hope this helps,
David

[Garrett K]

Hello PowerScore,

I found on this test that there were many questions that required diagramming. Even though I missed this question originally, I went back over it and got the correct answer. But can you please diagram this question for me, just so I can check my answer?

Thanks,
Garrett K

[David Boyle]

Hello PowerScore,

I found on this test that there were many questions that required diagramming. Even though I missed this question originally, I went back over it and got the correct answer. But can you please diagram this question for me, just so I can check my answer?

Thanks,
Garrett K

Hello Garrett K,

Just because bh fy, and fy 2s, doesn't mean that bh 2s. There may be many other types of houses on River Street that make up houses with front yards, so maybe they constitute the "most of the front-yard houses" that have 2 stories. We don't know that *any* brick house has 2 stories, actually.

Hope this helps,
David

[Zierra28]

when diagramming, I'd separated Brick House vs House because they seemed to be two diff categories. It wasn't until I'd diagrammed the other choices that I realized they were meant to be the same variable, and then D made sense as an answer. I might have run across it and just not noticed it before. Is this something that happens often, and if so how do I spot/avoid/successfully navigate it.

Thanks!