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 Rachael Wilkenfeld
PowerScore Staff
  • PowerScore Staff
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  • Joined: Dec 15, 2011
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#102340
Hi Jailena,

Personally, here I wouldn't diagram. I would instead look at what I know about books that are removed. However, it is possible to do with diagramming, and the diagramming can help focus on relationships.

There are a few different ways to diagram that second conditional. Adam recommends a nested conditional, and I really like that as an option. Another option is to make the issue of removal part of the sufficient condition. It's a little more complex to look at, but it's an option that can make sense.

(Local author OR SLH) AND Removed :arrow: checked out over the past three years


The idea is that if it falls into either the local author or of local history category, and it's removed THEN you know it hasn't been checked out in over three years.

Hope that helps!
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 zebrowski
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  • Joined: Jan 02, 2025
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#111280
Hi,

I am really exercised by this question.

By the law of contraposition and the De Morgan's laws, BR :arrow: BD and O2Y is logically equivalent to NOT BD or NOT O2Y :arrow: NOT BR. This reads, "if a book is not badly damaged or has been checked out for over two years, then it should not be removed from circulation."

Similarly, BR and (WLA or SLH) :arrow: O3Y is logically equivalent to NOT O3Y :arrow: NOT BR or NOT WLA and NOT SLH. This reads, "if a book has been checked out for over three years, then it either cannot be removed from circulation or else it is not written by a local author and is not significant to local history."

So we are given three sufficient conditions for when a book should not be removed from circulation: NOT BD (which translates as "not badly damaged"), NOT O2Y (which translates as "checked out for over two years" (because of double negation)) and NOT O3Y (which translates as "checked out within the past three years" (again, because of double negation)).

The answer choice says that "Paper Flowers" has been checked out within the last year. But this is not covered by the three sufficient conditions we are given. We don't know if "Paper Flowers" is badly damaged or not. We do know, however, that if it has been checked out within the last year, then it couldn't have been checked out for over two years, let alone for over three years. Why then shouldn't it be removed from circulation?

Thanks
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 zebrowski
  • Posts: 10
  • Joined: Jan 02, 2025
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#111286
Scratch that, NOT O3Y doesn't translate as "checked out within the past three years." This is the negation of this statement. NOT O3Y translates as "checked out for over three years."

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