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

  • $A \rightarrow B$
  • $A \rightarrow C$
  • $CD \rightarrow E$
  • $B \rightarrow D$
  • $E \rightarrow A$

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

  1. $CD \rightarrow AC$
  2. $BD \rightarrow CD$
  3. $BC \rightarrow CD$
  4. $AC \rightarrow BC$
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Answer is (B).

Apply membership test for all the given Functional Dependencies.

  1. $CD \rightarrow AC$
    $CD^+ = CDEAB$
  2. $BD\rightarrow CD$
    $BD^+ = BD$

i.e. $BD$ cannot derive $CD$ and hence is not implied.

Similarly do for rest two.

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