Arguing with words did not count as a valid counterexample unless you were sufficiently detailed and used variables to illustrate your arguments
You can justify this a variety of ways. Applying the closure to AC yields ABCD (which contains D). The transitive rule also works. Note that you can't reduce ABC->BD to AC->D by removing B from both sides - this is invalid.
This one is a little more tricky. Applying the transitive rule to A->B and B->C yields A->C. Applying the promotion rule to A->C then yields A->->C. Applying the complementation rule to A->->C then yields A->->BD. Some students presented less formal arguments regarding what happens when (B,D) values are swapped between tuples agreeing on A, given what you know about A->C. If clearly argued, these solutions received credit as well.