Which of the following option is not correct?
(A) {G → F, E → D, G → CE, BD → A} is a minimal cover for the set of functional dependencies {G → DF, E → D, GD → CE, BD → A}.
(B) {A → C, C → D, C → I, EC → A, EC → B, EI → C} is a minimal cover for the set of functional dependencies {A → C, AB → C, C → D, C → I, CD → I, EC → A, EC → B, EI → C}.
(C) {AB → C, D → E, E → C} is a minimal cover for the set of functional dependencies {AB → C, D → E, AB → E, E → C}.
(D) None of these.


Answer: (C)

Explanation: To find the minimal cover first remove the extraneous attribute and followed by removal of redundant FD.
(A) Removal of extraneous attribute:

{G → D, G → F, E → D, G → C, G → E, 
{here D was the extraneous attribute}, BD → A}

Removal of redundant FD,

Only G → D is redundant 

Therefore, minimal cover is,

{G → F, E → D, G → CE, BD → A} 

So, option is correct.

(B) After removing extraneous attributes from the FDs, given FDs are correct minimal cover of the original FDs. So, option is correct.

(C) As we can see {AB → E} is not covered in minimal cover since {AB}+ = ABC in the given cover {AB → C, D → E, E → C}. So option is false.

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