Question

Our conclusion is that the "fourth-floor lab must be cleaned out." Why? Because the director will support both proposals, and only those proposals the director supports will be approved. We also know that if Agnes's research proposal is approved, the fourth-floor lab must be cleaned out for her use, and if Immanuel's proposal is approved, he will continue to work in the second-floor lab. Let's diagram: If Agnes's proposal gets approved, then the fourth-floor is cleaned out. P1: APA ==> 4CO not 4CO ==> not APA If Immanuel's proposal is approved, then he will continue to use the second-floor lab P2: IPA ==> 2L not 2L ==> not IPA Only those proposals the director supports will be approved, i.e. if the proposal is approved, then the director supported it. P3: A ==> DS not DS ==> not A P4: The director supports both proposals. C: The fourth-floor lab must be cleaned out (aka "4CO") The issue here lies in the third premise. The proposal being approved is the sufficient condition. Thus, if a proposal is approved, it must have been supported by the director. However, merely knowing that the director supports it, does not necessarily lead us to the proposal being approved. Remember that the necessary conditions of the general principle and its contrapositive always form a possible scenario (DS and not A could occur together). That is why answer choice (B) is correct. The argument fails to consider the possibility that a proposal will be rejected even with the director's support. Hope that helps! Let us know if you have any other questions.

I missed P3. (B) now makes sense. Thanks a lot.

When you say: Remember that the necessary conditions of the general principle and its contrapositive always form a possible scenario (DS and not A could occur together) what lesson is that in?

@sharpen7 this discussion is in our Sufficient & Necessary lesson. It is highlighted during the discussion of the difference between "Either/Or" and "Not Both." Hope that helps! Please let us know if you have any other questions.