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If AD is the only candidate key for some relation R(A,B,C,D,E) then will CD → E be considered a partial dependency?

I think no , as for partial dependency to exist LHS of given dependency must be the proper subset of candidate key , but here CD is not subset of AD.
without seeing whole dependency of the relation we can not say about partial dependency okk

it can be partial dependency or can not be if in your relation dependency

if D generate C then it is partial dependency okk

This is a snippet from Fundamentals of Database Systems by Navathe. Let us look at the paragraph.

It is talking about full functional dependency, which we can see that if we remove of any attribute $A$ from $X$ in the functional dependency $X\rightarrow Y$, the dependency will become invalid.

OUR QUESTION;-

If AD is the only candidate key for some relation R(A,B,C,D,E) then will CD → E be considered a partial dependency?

Case 1:-

Remove $C$ from the functional dependency to check whether $D\rightarrow E$ is satisfying the functional dependency or not.

Since $AD$ is the only candidate key, $D$ cannot alone find $E.$

Case 2:-

Remove  $D$ from the functional dependency to check whether $C\rightarrow E$ is satisfying the functional dependency or not, and here also we cannot comment on this functional dependency.

Hence it is the case of full dependency, not partial dependency and we will not consider $CD\rightarrow E$ to be a partial dependency.

No,

The rule says partial dependencies are : prime attribute determined nonprime attribute.

here prime attributes are {A, D}, if A or D alone determined any other nonprime then it is partial dependencies.

in this case CD -> E, D is combined with C and determined E. So, CD becomes nonprime attributes.

CD →.E is nonprime → nonprime.
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