Self-study
Support On some hot days the smog in Hillview reaches unsafe levels, and Support on some hot days the wind blows into Hillview from the east. ██████████ ██ ████ ████ ████ ███ ████ █████ ████ ████████ ████ ███ █████ ███ ████ ██ ████████ ███████ ██████ ███████
Argument Summary
The author observes two things about hot days in Hillview. First, on some hot days, the smog reaches unsafe levels. Second, on some hot days, the wind blows in from the east. From these two premises, the author concludes that on some days when the wind blows in from the east, the smog reaches unsafe levels.
In other words, the author notices that "hot days" overlap with both "unsafe smog days" and "east wind days," and concludes that "unsafe smog days" and "east wind days" must also overlap with each other.
The Flaw
The author assumes that some of the hot days with unsafe smog are the same hot days with east wind. But that doesn't have to be true. The hot days with unsafe smog could be completely different days from the hot days with east wind.
Here's what might be true:
Notice that the premises are still satisfied: some hot days have unsafe smog (left overlap), and some hot days have east wind (right overlap). But the unsafe smog days and east wind days are on completely different hot days. So the conclusion that some east wind days have unsafe smog doesn't logically follow.
Here's the abstract version of this flaw: Even if “Some A are B” and “Some A are C,” we cannot conclude “Some B are C.” This is because B and C might not overlap within A.
20.
The reasoning in the argument ██ ██████ ██ ████ ███ ████████
a
mistakes a condition ████ █████████ ███████████ ██████ ██████ ██ ████ ███ █ █████████ ████ ███████████ ███████████ ██████ ██████ ██ ████
You might be drawn to (A) because it mentions something that "sometimes accompanies" unsafe smog, which sounds like the east wind. But the author doesn't think that the east wind necessarily accompanies unsafe smog. The conclusion just says that on some east wind days, the smog reaches unsafe levels.
It's possible you think the condition that "sometimes accompanies" unsafe levels of smog is hot days. But even then, the author doesn't assume that hot days necessarily accompany unsafe smog levels.
b
fails to recognize ████ ███ ███ █████ ████ ████ ███████ ██ ██████ ████ ████ ██ ███ ██████ ████ ██████ █████ ███ █████ ████ ████ ██ ███████ ██ ██████ ████ ████ █████
This accurately describes the flaw using the language of sets. The "one set" is hot days. The "two others" (meaning two other sets) are unsafe smog days and east wind days. Hot days has members in common with each of those two sets (some hot days have unsafe smog, and some hot days have east wind). But the argument fails to recognize that unsafe smog days and east wind days might have no members in common with each other, as illustrated in the second diagram above.
c
uses the key ████ ████████ ██ ███ █████ ██ █ ███████ ███ ██ ███████ █████ ██ ███ ██████████
"Unsafe" means the same thing in both the premise and the conclusion: the smog has reached a level that isn't safe. There's no shift in meaning.
d
contains a premise ████ ██ ███████████ ██████ ███ ██████████ ██ ████████ ██ ██ ████
This describes circular reasoning. But the premises aren't circular. We can accept that some hot days have unsafe smog and that some hot days have east wind without already believing the conclusion. These premises describe separate observations that don't depend on the conclusion being true.
e
infers a particular ██████ ████████ ████ █ ███████████ ████ █████ ██ █████████ ██ █ ███████ ██ █████ ████
You might be drawn to (E) because the argument involves two things (east wind and unsafe smog) that coincide with a third thing (hot days), which can look like a correlation. But the argument doesn't claim that east wind causes unsafe smog or that unsafe smog causes east wind. The conclusion is just that both happen on the same day sometimes.