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 → CD — 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.
CD → AC
- B.
BD → CD
- C.
BC → CD
- 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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