If Agnes's research proposal is approved, the fourth–floor lab must be cleaned out for her use. Immanuel's proposal, ...

shunhe on May 29, 2020

Hi @mkonovodoff,

Thanks for the question! So the issue here is that this is a flawed reversal, and we can walk through the logic to find out why. Let me diagram the first three sentences very quickly (we don’t diagram the second since it’s not helpful):

Agnes proposal approved —> 4th-floor lab cleaned out
Immanuel’s proposal approved —> continue to work in 2nd floor lab

Now we get to the sentence you pointed out: Only those proposals the director supports will be approved. Remember that we diagram “X only if Y” as X—>Y. In other words, we diagram this sentence

Project approved —> Director supports

And if we think about ways we can reword the original statement, this makes sense. If a project was approved, that means the director has to have supported it. Why? Because only the proposals he supported would be approved! It’s not necessarily the case the other way around. It’s possible that the director supports a project that doesn’t ultimately be approved. But something that’s necessary for approval is the director’s support. It’s necessary, but not sufficient.

But then we get the following:

Director supports proposals —> Fourth-floor lab cleaned out

And this is only true if you think the following

Director supports —> Project approved

Which, as just mentioned, mixes up the sufficient and necessary terms. In ordinary English, it fails to consider that the director might support some projects that are ultimately rejected, and this is what (B) tells us, which is why (B) is the correct answer.

Hope this helps! Feel free to ask any other questions that you might have.