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R (A, B, C ,D ,E )

F={ A->B, BC-> D, D->BC, B->E, B->A }

Check whether BD is  C.Key or S.key . Also find the candidate key.

2 Answers

Best answer
5 votes
5 votes

BD+ ={BDEAC}

D+={DBCEA} 

Since D alone is Ck implies BD is super key

Candidate Keys

D+={ABCDE}                 By replacing D with BC

BC+={ABCDE}               By replacing B with A

AC+={ABCDE}

These are candidate keys D,AC,BC

edited by
6 votes
6 votes

Ck with single attribute :

D+ =ABCDE            // This is the only Ck with single attribute

Ck with 2 attributes :

AC+ =ABCDE

BC+ =ABCDE          // These are the only 2 Ck's with 2 attributes

There is no Ck with 3 attributes :

There is no Ck with 4 attributes :

Now your question whether BD is a Ck Or Sk

you can see that D is already proven to be Ck So BD will be a Sk Here not a Ck .

edited by

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