An organization needs to maintain database having five attributes \(A, B, C,…
2019
An organization needs to maintain database having five attributes \(A, B, C, D, E\). These attributes are functionally dependent on each other for which functionality dependency set \(𝐹\) is given as: \(F:\{A→BC,D→E,BC→D,A→D\}\). Consider a universal relation \(R(A, B, C, D, E)\) with functional dependency set \(𝐹\). Also all attributes are simple and take atomic values only.
Identify primary key of table 𝑅 with functional dependency set 𝐹
- A.
BC - B.
AD - C.
A - D.
AB
Attempted by 798 students.
Show answer & explanation
Correct answer: C
Compute the closure of the attribute set A to check if it is a key:
Start with A+: {A}.
Use A → BC to add B and C: now A+ = {A, B, C}.
Use BC → D to add D: now A+ = {A, B, C, D}.
Use D → E to add E: now A+ = {A, B, C, D, E}.
Since A+ includes all attributes of R, the attribute set A is a superkey. It is also minimal (it has no proper subset), so A is a candidate key (primary key).
Quick notes on the other attribute sets:
BC: BC → D and D → E give BC+ = {B, C, D, E}, but A is not determined, so BC is not a key.
AD and AB: both determine all attributes because they include A, but they are not minimal since A alone is sufficient. Therefore they are superkeys but not candidate (primary) keys.
Conclusion: The primary (candidate) key for R is the single attribute A.
A video solution is available for this question — log in and enroll to watch it.