# GATE2005-78

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Consider a relation scheme $R = (A, B, C, D, E, H)$ on which the following functional dependencies hold: {$A \rightarrow B$, $BC \rightarrow D$, $E \rightarrow C$, $D \rightarrow A$}. What are the candidate keys R?

1. $AE, BE$
2. $AE, BE, DE$
3. $AEH, BEH, BCH$
4. $AEH, BEH, DEH$

edited

(d) AEH, BEH, DEH

using the given functional dependencies and looking at the dependent attributes, E and H are not dependent on any. So, they must be part of any candidate key. So, only option is D. If we see the FD's, adding A, B or D to EH do form candidate keys.

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