Candidate key

Question

how many number of candidate keys in the following relation r = (a, b, c, d, e, h) on which the following functional dependencies hold: {a →bc, c d→ e, e → c,d → aeh,abh→ bd, dh → bc}. what are the candidate keys r?

Comments

I think 3 candidate keys are there, d, abh, aceh

Answer 1

CK are {d, abh and aceh}

Comments

Why abh a ck? We can derive b from a.

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Using closure set of abh we can derive all attributes, as

abh⁺  =  abhcde

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abh is a super key.

We can derive all attributes using only ah.

Answer 2

2 candidate keys

D and ah

Answer 3

[d, abh and aceh] are candidate keys.

Candidate keys are those keys which can determine all attribute of a relation..

Comments

only two candidate keys are possible.

D and AH