UYZ,VYZ,XYZ

Option (D)

Option (D)

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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?

- $UY, VY$
- $UY, VY, XY$
- $UYZ, VYZ, VWZ$
- $UYZ, VYZ, XYZ$

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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

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