Find the candidate key(s) of the relation R(UVWXYZ) with FD set F = {UV → W,…

2015

Find the candidate key(s) of the relation R(UVWXYZ) with FD set
F = {UV → W, XW → Y, U → XZ, Y → U}

  1. A.

    XW

  2. B.

    UV, YV and WXV

  3. C.

    YUV, XV and WV

  4. D.

    None of these

Attempted by 153 students.

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Correct answer: B

To find the candidate keys, first identify attributes that do not appear on the right-hand side of any functional dependency. Here, V is the only such attribute, so every candidate key must include V. Next, compute closures for combinations involving V to see which determine all attributes {U,V,W,X,Y,Z}. The closure of UV includes U, V, and via dependencies yields all attributes. Similarly, YV determines U (via Y→U), which leads to all attributes. WXV also determines all attributes through the given dependencies. Thus, the candidate keys are UV, YV, and WXV.

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