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}

  1. A.

    A

  2. B.

    AE

  3. C.

    BE

  4. 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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