I have a question about this:

Suppose we have relation R(A, B, C, D, E) , with some set of FD’s, and we wish to project those FD’s onto relation S(A,B,C). Give the FD’s that hold in S if the FD’s for R are:

A-> D, BD->E, AC->E, and DE->B

When finding closure for all of them, I find that there is no minimal basis for S, though am not sure. What do you guys think?

That's right.

But the issue is, you may have normalised the FDs in the relations (each within themselves) but you haven't normalised the FDs (all columns and FDs) together; you haven't normalised the relations together, to produce a database. When you do that, the conflicts will disappear.