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GO Classes DPP | GATE CS, DA | DBMS | BCNF Decomposition

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Consider $R(A,B,C,D,E,F)$ with $F=\{A\to B,\ A\to C,\ BC\to E,\ BC\to D,\ E\to F,\ BC\to F\}$.

Suppose the following BCNF decomposition is used:

$R_1(B,C,E)$

$R_2(B,C,F)$

$R_3(B,C,D)$

$R_4(A,B,C)$

Which original functional dependency is not dependency preserved?

  1. $A\to B$
     
  2. $BC\to D$
     
  3. $BC\to E$
     
  4. $E\to F$

1 Answer

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Check the dependencies one by one.

$A\to B$ can be enforced inside $R_4(A,B,C)$.

$BC\to D$ can be enforced inside $R_3(B,C,D)$.

$BC\to E$ can be enforced inside $R_1(B,C,E)$.

Also, $BC\to F$ can be enforced inside $R_2(B,C,F)$.

Now consider $E\to F$.

$E$ appears in $R_1$.

$F$ appears in $R_2$.

No single component contains both $E$ and $F$.

More importantly, starting from $E$ using the union of the projected FDs does not allow us to derive $F$.

$\therefore E\to F$ is not dependency preserved.
 

Answer : D

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