assuming the Derived Subjects Hypothesis and the Case Filter, give derivations for the following sentences. For each derivation, name whether it is a nominative case, genitive case, or accusative case that is used to produce one parse from another, and explain why that rule is necessary. That is$,$ say what principle$($s$)$ of the grammar would be violated if that rule

were not used.

$(1)$ Smith should put them in the box.

$(2)$ Smith will make some coffee boil.

$(3)$ The kids could be happy.

$(4)$ The kids might appear happy.

$(5)$ She must believe them to appear happy.