As I am looking at your problem sets, I am reminded of Irene’s admonition about the importance of clarity in semantic argumentation. Here is the quote (from her 24.970 lecture notes):

When arguing for or against a particular semantic analysis, we often proceed by showing that this analysis makes correct or incorrect predictions about the truth conditions of certain examples. To make such arguments, you need to be able to compute what a given analysis predicts for a given sentence. Computations of this sort are the basic building blocks of all arguments in formal semantics. In the published literature, you will not find many of them spelled out. When you listen to professionals debating, it may even look as if they see the predictions of each proposal instantly without ever having to compute anything. But these appearances are deceptive. What is really going on is that formal semanticists write for and talk to a trained audience. As part of the training they presuppose, you have already done so many calculations that almost every new one you encounter will be a minor variant or combination of things that you have computed before. Until you get to this stage, however, you have to go slowly, take one step at a time, and pay meticulous attention to how each step is supported by the definitions, rules, and assumptions that comprise the analysis under consideration.