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Consider a relation R(A,B,C,D,E) with the following functional dependencies:
ABC -> DE and
D -> AB
The number of superkeys of R is:
a) 2
b) 7
c) 10
d) 12

1 Answer

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ABC->DE

D->AB

Candidate keys of these FD's are ABC and CD

Number of super keys with ABC are ABC _ _ =4

Number of superkeys with CD are _ _ CD_ =8

Total number of superkeys =n(ABC U CD)=n(ABC)+n(CD)-n(ABC ∩ CD)

since ABCD ,ABCDE are common in both keys so n(ABC ∩ CD) =2

                                                                   = 4+8-2 =10

Therefore total number of superkeys are 10
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