Identify the minimal key for relational scheme R(A, B, C, D, E) with…
2014
Identify the minimal key for relational scheme R(A, B, C, D, E) with functional dependencies F = {A → B, B → C, AC → D}
- A.
A
- B.
AE
- C.
BE
- D.
CE
Attempted by 1025 students.
Show answer & explanation
Correct answer: B
Minimal key: AE
Explanation and steps to determine it:
Compute the closure of AE: start with {A, E}.
From A → B add B, giving {A, B, E}.
From B → C add C, giving {A, B, C, E}.
From A and C → D add D, giving {A, B, C, D, E} which is all attributes. Thus AE is a superkey.
Check minimality: A+ = {A, B, C, D} (missing E), and E+ = {E}. Neither A nor E alone determines all attributes, so AE is minimal.
Therefore the minimal key for R with the given functional dependencies is AE.
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