database - Does union of candidate keys together form a candidate key?

Question

Relation R consists of columns {A,B,C,D}. A uniquely defines a tuple. So does B. A and B are candidate keys, since they are minimal. What about a set {A,B}? {A,B} together uniquely defines a tuple, but it is not minimal.

What is the term for {A,B}. Usually non-minimal candidate keys are called super keys. Is there a special name for a union of candidate keys?

EDIT:

Excuse me for imprecise question. It can indeed be clearer. As far as I understand, key == candidate key == minimal set of attributes that uniquely define a tuple.

标签： databasedatabase-design

Answer 1

The union of candidate keys K1 and K2 yields a candidate key iff K1=K2, that is, if they are in fact the very same key. In all other cases, it will by definition yield a (super)key that isn't irreducible, and if your definition of "candidate key" is that it is an irreducible (super)key then (the result of) that union is obviously no longer a candidate key.

As for keys terminology, I think most respectable (there are others too) textbooks stick to the convention :

"superkey" = just any key
"candidate key" = irreducible (=minimal) superkey
non-minimal superkey = "proper superkey" (and not just "superkey" as you stated)
"key" is supposed to be used as synonym for "candidate key" but the linguistics of the word cause it to often also be used with the meaning of "just any key". Beware !

And no, I don't think there is a special term for the particular kind of proper superkey that happens to be a union of two (or more) candidate keys. There is no useful purpose in ever knowing such a thing about a key.