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GO Classes DPP | Databases | Functional dependency | JMU

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5 5 votes
Consider a relation R(A, B, C, D, E, F, G, H, I, J) with functional dependencies:

$$
\mathrm{AB} \rightarrow \mathrm{C}, \mathrm{BD} \rightarrow \mathrm{EF}, \mathrm{AD} \rightarrow \mathrm{GH}, \mathrm{~A} \rightarrow \mathrm{I}, \mathrm{H} \rightarrow \mathrm{~J} .
$$

Which of the following is a candidate key for R ?
A) $A B D$
B) $A B D H$
C) $A D$
D) $A B D I$

3 Answers

2 2 votes
$\mathrm{ABD}^{+}=\{\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}, \mathrm{F}, \mathrm{G}, \mathrm{H}, \mathrm{I}, \mathrm{J}\} \Rightarrow$ all attributes covered.
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0 0 votes
ABD+ = {A,B,D}

           = {A,B,D,C,E,F,G,H}    Since AB => C and BD => EF and AD => GH

           = {A,B,D,C,E,F,G,H,I,J}    Since H => J and A=>I

So ABD is a candidate key Option A is True.
0 0 votes

A,B,D are not present Right hand side of any of the function dependency that means ABD is must be part of CK and as we know that if ABD itself is the candidate key that's means adding something to it will make it sk not candidate key and if you are going to remove somthing from ABD then it will not become ck 

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