Test by Bikram | Mock GATE | Test 3 | Question: 38

Question

Consider a relation $R$$\left ( A, B,C,D, E  \right  )$ with the following $FD$ set $F$:

 $A\rightarrow BC$
 $CD\rightarrow E$
 $B\rightarrow D$
 $E\rightarrow A$

The canonical cover of the above $FD$ set is:

• A.   $A\rightarrow BC$, $C\rightarrow E$ , $B\rightarrow D$ , $E\rightarrow A$
• B.   $A\rightarrow BC$ , $CD\rightarrow E$ , $B\rightarrow D$ , $E\rightarrow A$
• C.   $A\rightarrow B$ , $CD\rightarrow E$ , $BC\rightarrow D$ , $E\rightarrow A$
• D.   $A\rightarrow BC$ , $B\rightarrow E$ , $B\rightarrow D$ , $E\rightarrow A$

Answer 1

No extra attributes and no FD is redundant in the given FD set, hence its canonical cover is given FD set itself .

Comments

@Bikram sir, i think (A) is also canonical cover.

plz check it

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@bittu In option A, $C$ closure gives $EABC$ but in the given FD set, $C$ closure gives $C$ only. 

A canonical cover of a set of functional dependencies $F$ is a simplified set of functional dependencies that has the same closure as the original set $F$.