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#15 - Zack's Coffeehouse schedules free poetry readings

rachue
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I need help understanding why E is incorrect and D is correct. Aren't they saying the same thing? Thanks in advance.
Dave Killoran
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These two are easy to confuse, and students tend to pick (E) almost as frequently as (D), which tells you this is a tough question.

According to the stimulus, Zack's offer free poetry readings almost every Wednesday (Wednesday most → P).

The stimulus also indicates that when a poetry is scheduled, then half-priced coffee is offered all day (P → 1/2PC). Note that this allows for Zack's to offer half-priced coffee on other days as well, including Wednesdays without a poetry reading (hence the "if not all Wednesdays" in answer choice (D)).

Answer choice (D): This must be true, and is thus the correct answer. Poetry readings occur on most Wednesday (meaning half-priced coffee, and it is possible that on the other days Zack's offers half-priced coffee as well).

Answer choice (E): This does not say the same thing as (D). (D) is about coffee being offered whereas (E) is about when coffee is not offered. In this case, is there proof that Zack's doesn't offer coffee on some Wednesday? No, and thus (E) is incorrect.

Please let me know if that helps out. Thanks!
Dave Killoran
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rachue
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That helps me see why D is correct but at the same time, if it says in the stimulus that free poetry readings are "almost every Wednesday," doesn't that imply that there are some Wednesdays that no free poetry readings are offered? Doesn't "almost" mean "not all"? And if so, wouldn't E then be correct?
Dave Killoran
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Answer choice (E) is about coffee, not about poetry, so whether or not there is a poetry reading on a Wednesday, Zack's can still offer half-priced coffee.

What's occurring is that you are making a Mistaken Negation, by thinking that when there is no poetry, then there is no half-priced coffee. But that doesn't have to be true, so Zack's could offer half-priced coffee every Wednesday, and therefore answer choice (E) cannot be inferred.

Does that make sense? Please let me know. Thanks!
Dave Killoran
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rachue
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It helps but I still don't see how D is 100% solid. "Almost every Wednesday" implies by its nature NOT every Wednesday, just most Wednesdays. So how can D's "Zack's offers half-priced coffee all day on most if not all Wednesdays" be correct?

Also, this is the correct diagram, right?

Wednesday (almost) --> free poetry --> 1/2 priced coffee

And if that is the correct diagram, isn't E also about poetry, too, and not just coffee, and therefore "almost every Wednesday" applies?

I understand now why E is incorrect but I"m still shaky on why D is for sure correct, especially with the ending "if not all Wednesdays" part.

Thanks again for the help.
Dave Killoran
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Answer choice (D) is bulletproof, and understanding the concept behind this answer choice is critical, so let's go back to the portion of my previous post that indicates that it appears you are making a Mistaken Negation.

Let's first condense the statement about Wednesdays, poetry, and coffee to:

Wednesday Poetry→ 1/2 priced coffee

Yes, that is stronger than what the stimulus says, but let's just go with that for a second. Under that relationship, we have 1/2 priced coffee every Wednesday. But, the stimulus doesn't say "every," it says ""almost every," and let's say that that clearly means some Wednesdays don't have poetry readings. If you then take that to mean that those Wednesday don't then have 1/2 priced coffee, what you are saying is this:

not Wednesday Poetry → not 1/2 priced coffee

But that's a false inference (in this case, a Mistaken Negation): just because some Wednesdays don't have poetry readings doesn't also mean that there isn't 1/2 priced coffee on those days. Maybe Zack's runs a special on the days without poetry readings that gives consumers 1/2 priced coffee.

So, we know that on most Wednesdays Zack's offers 1/2 priced coffee, and it is possible that on the Wednesdays without poetry there is also 1/2 priced coffee. Abstractly, when the sufficient condition occurs, we know the necessary also occurs, but it is also possible that the necessary condition can occur when the sufficient condition has not occurred. that understanding of the last part is what is being tested in (D).

If that's not entirely clear, consider the following analogy:

On most but not all Wednesdays I go to work, and whenever I go to work I wear shoes.

What about the Wednesdays I don't go to work? Is it possible for me to wear shoes? Yes, definitely, so we can infer that on "most if not all Wednesdays" I wear shoes.

Does that help?
Dave Killoran
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rachue
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YES! Tremendously! I get it now! THANK YOU!
stsai
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Q15 "Zack's Coffeehouse schedules free poetry readings..."
I am not particularly strong with this kind of questions, so I handled it with caution, eliminated (A) and (B). I chose (E) in the end because I thought "almost every Wednesday" is the same as "On some Wed...does not..."
It would be great if I can see the proper reasoning of each answer choices, so that I know how to correctly tackle this type next time.

Thank you!
Eric Ockert
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15. The logic of the stimulus is:

Wed --most----> Poetry Readings --------> 1/2 Price Coffee

(Most Wednesdays have Poetry Readings and all Poetry Readings have 1/2 Price Coffee)
So, the conclusion you can make is that Wed ----most-----> 1/2 Price Coffee
(Most Wednesdays have 1/2 Priced Coffee)

Answer D is essentially saying this exact thing. "MOST" indicates "more than half", and would include the POSSIBILITY of ALL. In other words, it is POSSIBLE that Zach's offers coffee on every Wednesday, but you do not know for sure.

E is incorrect because, while you know that Zach's offers 1/2 price coffee on most Wednesdays, he might offer it on all Wednesdays, so you can't say for certain that he ever does NOT offer 1/2 price coffee.

A is incorrect because you have no idea whether Wednesday is "the most common day" or not.

B is similar to a Mistaken Reversal. Just because you know that

Wednesday ---most---> 1/2 price coffee

does NOT mean you know: 1/2 price coffee -----most -----> Wednesday

"most" is NOT a reversible idea.

C is incorrect as well. You know that "All Poetry Readings have half priced coffee", but that does not mean "All half priced coffee has poetry readings" or "almost every half priced coffee has poetry readings". All you could say for certain is that "Some days with half priced coffee have poetry readings"

Hope that helps!
Eric Ockert
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stsai
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Now I get it!
For #15, I need to review the Formal Logic section of the bible, since I forgot that "most" could be "possibly all."


Thanks so much Eric!