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#20 - On some hot days the smog in Hillview reaches

JKing
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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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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.
Jon Denning
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Jiya
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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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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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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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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.
Adam M. Tyson
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lilmissunshine
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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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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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That's what I would call it, gen. Any time you presume the truth of the conclusion, that's circular reasoning.
Adam M. Tyson
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gen2871
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Coolio. thank you!