GATE | GATE CS 2013 | Question 54

Relation R has eight attributes ABCDEFGH. Fields of R contain only atomic values. F = {CH -> G, A -> BC, B -> CFH, E -> A, F -> EG} is a set of functional dependencies (FDs) so that F+ is exactly the set of FDs that hold for R.

How many candidate keys does the relation R have?

(A) 3
(B) 4
(C) 5
(D) 6


Answer: (B)

Explanation: A+ is ABCEFGH which is all attributes except D.

B+ is also ABCEFGH which is all attributes except D.

E+ is also ABCEFGH which is all attributes except D.

F+ is also ABCEFGH which is all attributes except D.

So there are total 4 candidate keys AD, BD, ED and FD

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