A relation R = {A, B, C, D, E, F} is given with following set of functional…
2006
A relation R = {A, B, C, D, E, F} is given with following set of functional dependencies:
F = {A→B, AD→C, B→F, A→E}
Which of the following is candidate key?
- A.
A
- B.
AC
- C.
AD
- D.
None of these
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Correct answer: C
To find the candidate key, identify attributes that do not appear on the right-hand side of any functional dependency. Here, A and D are never on the RHS, so they must be part of the key. Calculate the closure of AD: A→B and A→E add B and E to get {A,B,D,E}. AD→C adds C. B→F adds F. Thus, (AD)+ = {A,B,C,D,E,F}. Since A alone yields {A,B,E,F} (missing C and D), AD is the minimal candidate key.
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