3NF Decomposition - I'm not sure about this example
The theory is all fine and good, but it only starts to really make sense once you understand the practice. The Lawyer's version of the first three Normal Forms is:


The Key - there must be a Primary key for every relation being normalized.
The Whole Key - There must not be any functional dependencies of attributes on any proper subset of the Primary Key.
And Nothing but The Key - There must not be any functional dependencies of attributes on non-key attributes.


In practice relations frequently have multiple candidate keys, and these rules must apply to all of them in turn.

Also, when Normalizing one must determine the minimal key(s) for each relation, and use those rather than any Super Key.

Your lecturer didn't remove the fifth column altogether because the functional dependency in that column still exists, and must still be accounted for in the Normalization process.

Update:

The FD AD->C doesn't disappear by virtue of recognizing ADC as a subset of CDA; neither is it sensible to have two relations ADC and CDA both in the model as this is a redundancy of exactly the sort Normalization is designed to eliminate.