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Consider a relational schema $S=(U,V,W,X,Y,Z)$ on which the following functional dependencies hold:

$(U \rightarrow V, VW \rightarrow X, Y \rightarrow W, X \rightarrow U)$

Which are the candidate keys among following options?

  1. $UY, VY$
  2. $UY, VY, XY$
  3. $UYZ, VYZ, VWZ$
  4. $UYZ, VYZ, XYZ$
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UYZ,VYZ,XYZ

Option (D)

1 Answer

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Given FD

 U->V  , Y->W,  X->U, VW->X  SO

{UY}+->VWXUY

 everything  except Z in relation so add Z too to get relation S  i.e {UYZ}

similarly {VY}+ ->VYWXU  again add Z  {VYZ}

also {XY}+ ->VWXU  again add Z     {XYZ}

so ans is 4

note:- VWZ wont give  Y hence 3 is incorrect

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