Higher normal form that this relation satisfies

Let R{A,B,C,D,E} be a relation with functional dependencies:

B->EA
EBC->D
BED->A

Question: What's the higher normal form that R satisfies?

Attempt:

• 1NF: satisfied, since all the attributes are defined as single-valued.
• 2NF: I'm not exactly sure. 2NF states that there must not be partial dependecies. The candidate key is BC, so is B->EA considered a partial dependency or does it have to be one attribute on the rhs?
• 3NF: Assuming 2NF is satisfied, then for the dependency: B->EA, B is not a superkey and E,A are not prime attributes. Thus, 3NF is not satisfied.

Why (or why not) the 2NF is satisfied?

B -> EA

is equivalent to the two dependencies:

B -> E
B -> A

for the decomposition rule. Since neither E nor A are prime attribute and B is a proper subset of a candidate key, the relation is not in 2NF.