In a schema with attributes A, B, C, D and E following set of functional…

2005

In a schema with attributes A, B, C, D and E following set of functional dependencies are given

A → B A → C CD → E B → D E → A

Which of the following functional dependencies is NOT implied by the above set?

Answer: B. BD → CDTest each dependency by computing attribute closures: CD → AC: CD+ starts as {C,D}. CD → E adds E; E → A adds A; A → B and A → C add B and C. So CD+ contains…

  1. A.

    CD → AC

  2. B.

    BD → CD

  3. C.

    BC → CD

  4. D.

    AC → BC

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Correct answer: B

Test each dependency by computing attribute closures:

  • CD → AC: CD+ starts as {C,D}. CD → E adds E; E → A adds A; A → B and A → C add B and C. So CD+ contains A and C, hence CD → AC is implied.

  • BD → CD: BD+ starts as {B,D}. From B → D we already have D. No FD produces A, C, or E from B and D alone, so C is not in BD+. Therefore BD → CD is not implied.

  • BC → CD: BC+ starts as {B,C}. B → D adds D, so BC+ contains C and D. Thus BC → CD is implied.

  • AC → BC: AC+ starts as {A,C}. A → B adds B; with B → D you also get D. So AC+ contains B and C, meaning AC → BC is implied.

Conclusion: BD → CD is the only dependency not implied by the given set because C cannot be derived from B and D.

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