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Consider a relational schema R = (A, B, C, D, E, H) on which the following functional dependencies hold: {A → B, BC → D, E → C, D → A}. What are the candidate keys of R?
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- AE, BE
- AE, BE, DE
- AEH, BEH, BCH
- AEH, BEH, DEH
- AE, BE
Correct Option: D
A → B, BC → D, E → C, D → A
We start form set of all the attributes and reduce them using given functional dependences
ABCDEH ABCDEH
ABCEH {BC- → D}
ABEH{E → C} BCDEH {D → A}
AEH {A → B} BEH {E → C}
ABCDEH ACDEH {A → B} ADEH{E → C} DEH{D → A}
So candidate keys are AEH, BEH & DEH .
