Quick Refresher:
1) Proper subset of A = subset of A which doesnot includes all the elements of A.
Eg: A = {a,b}
subsets: null, {a}, {b}, {a.b}
proper subsets: null, {a}, {b}
2) Prime Attribute is an attribute that is part of a candidate key.
Eg: If R{A,B,C,D} and
AB and BC are candidate keys, then:
prime attributes = A,B,C
non prime attributes = D
Back to Basic:
0) A-> BC can be decomposed to A->B and A-> C
but
AB->C can't be decomposed into A->C and B->C.
1) Therefore, From 0) we come to know that we can't decompose ADE into A, D and E. We have treat it as a single unit.
2) Partial Dependency exists if:
(proper subset of candidate key) -> (non prime attribute)
Back to your Doubt:
ADE->C //assuming C is nonprime
^
|
|________ ADE as a whole (refer pt. 1 of Back to Basic) is not proper subset of candidate Key AB.
Therefore, Partial Dependency doesn't holds.
Hence in 2NF. (ofcourse assuming already in 1NF.)
Different scenario:
Assume AB is candidate key and C is non prime attribute.
then, A -> C and B -> C will lead to partial dependency,
^ ^
| |_________ non prime attribute
|
proper subset of candidate key AB.
