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 Administrator
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#84801
Complete Question Explanation


Flaw in the Reasoning—Formal Logic. The correct answer choice is (B)

The premises of the argument contain a Formal Logic setup:

     HD = hot days in Hillview
     SUL = smog reaches unsafe levels
     WBE = wind blows in from the east
Capture.PNG
The combination of two “some” statements does not yield
any inferences. Yet, the author draws a conclusion ( SUL :some: WBE ) on the basis of the
relationship and you must identify the answer that explains why this conclusion is incorrect.

Answer choice (A): There is no proof in the argument that the condition of WBE sometimes
accompanies smog reaching unsafe levels—that is the mistake made by the author. The answer
would be more attractive if it read as follows:

     “mistakes a condition (WBE) that sometimes accompanies hot days in Hillview for a
     condition that sometimes accompanies unsafe levels of smog”

Answer choice (B): This is the correct answer. When two “some” statements are joined, no inference
can be drawn because the group common to both may be large enough that the two sub-elements
do not overlap. For example, let’s say there are 10 hot days in Hillview (HD), 1 day when the smog
reaches unsafe levels (SUL), and 1 day when the wind blows in from the east. Is it necessary that
the 1 day when the smog reaches unsafe levels is the same day that the wind blows in from the east?
No, but the argument concludes that is the case, and that error is described in this answer choice. For
reference purposes, here is the answer choice with each abstract item identified in parentheses after
the reference:

     “fails to recognize that one set (HD) might have some members in common with each of two
     others (SUL and WBE) even though those two other sets (SUL and WBE) have no members
     in common with each other”

Answer choice (C): This answer choice describes the Uncertain Use of a Term, but the argument is
consistent in its use of “unsafe.” Therefore, this answer is incorrect.

Answer choice (D): Each premise is plausible regardless of the truth of the conclusion.

Answer choice (E): The argument does not feature causal reasoning. The conclusion clearly states
that the two events happen together, but there is no attempt to say that one caused the other. If you
chose this answer, try to identify the causal activators in the argument—there are none.
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 JKing
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#9047
HDsomeSUL
HDsomeWBE
--------------
WBEsomeSUL

AsomeB
AsomeC
--------
CsomeB

Bad Argument

The answer is B. The wording slightly confused me. What it means is that HD has something in common with SUL and WBE. However SUL and WBE do not have anything in common? Therefore, WBEsomeSUL really has no commonality?
 Jon Denning
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#9075
Hey J - thanks for the question. Your diagrams, both specific and generalized, look correct, and from that you can see the flaw: you cannot connect two "some" statements and draw any kind of inferences, "some" or otherwise.

This type of mistake depends on the assumption that the group common to some of the other two (hot days here) implies that the other two have some in common with each other, but this does not have to be the case. And that's exactly what B states: one set (HD) may have something in common with each of two other groups (SUL and WBE), even though those two groups have nothing in common (no overlap between SUL and WBE, which is the mistake made in the conclusion where the authors assumes they do have "some" in common).

Make sense? The wording is tricky because it generalizes things as "one set" and "members in common" instead of saying "hot days" and "some have unsafe smog levels/some have winds from the east," but the error itself is simply that two groups connected via "some" with a third, common/shared group cannot be definitively connected to each other.
 Jiya
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#16331
This one feels familiar but I cannot seem to locate it if it's been explained before - sorry in advance if this is a duplicate!

How do we arrive at B for the correct answer? I selected E and was pretty confident I had it right!
 David Boyle
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#16338
Jiya wrote:This one feels familiar but I cannot seem to locate it if it's been explained before - sorry in advance if this is a duplicate!

How do we arrive at B for the correct answer? I selected E and was pretty confident I had it right!
Hello Jiya,

There's not necessarily anything causal here, so answer E doesn't work.
Answer B is right because while one set (Hillview) may sometimes participate in two other sets (unsafe smog and hot wind), that doesn't mean that those two sets ever intersect. Maybe, for example, the hot wind blows away all the unsafe smog.

Hope this helps,
David
 lilmissunshine
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#46684
Hello,

I wanted to ask why (A) is incorrect. Is it because of "sometimes" and the condition could be "never"?

Many thanks!
 Adam Tyson
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#46909
These is a condition that sometimes accompanies unsafe smog levels, lilmiss, and that condition is "hot days". The problem with answer A is that the author does not conclude that when there are unsafe levels it must be hot! That would be pretty close to making a Mistaken Reversal, which is not the flaw here. Instead, the flaw is one of Formal Logic, presuming that because one condition (hot days) sometimes coincides with another condition (unsafe smog) and sometimes coincides with a third condition (wind blowing from the east) that it must sometimes coincide with both at once. Those two other conditions could be mutually exclusive.
 lilmissunshine
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#46918
Hi Adam,

Thanks for explaining! I definitely misinterpreted answer (A) initially. I thought the "condition that sometimes accompanied unsafe levels of smog" was "the wind blows"... But that wouldn't make any sense for the necessary condition. I actually drew a Venn Diagram the first time and easily chose (B).
 gen2871
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#49238
Hi, I wonder what is flaw is the wording of answer choice D indicating? it says contains a premise that is implausible unless the conclusion is presumed to be true.

premise plausible :arrow: conclusion true.

sounds like circular reasoning because the CP would be Concl. not true :arrow: premise implausible. Thank you!
 Adam Tyson
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#49325
That's what I would call it, gen. Any time you presume the truth of the conclusion, that's circular reasoning.

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