Keys of a relation

I got relation: > R = { (ABCDEF) , (A B F -> C, B C -> F, F -> A, F -> B, D E -> E, E -> D)} keys of this relation are: > {BCE}, {EF} But I don't get it... why? Why not only {EF}.. it got less attributes than {BCE}.. Another example, relation: > R2 = {(ABCDEF), (A -> B C , B -> D , E -> F)} and the key is: > {AE} why only one? Why not: > {AE}, {ABE} ABE also determines all other attributes, why is it not a key?