Q39.Marks: +2.0UGC NET Paper 2: Computer Sc 23rd August 2024 Shift 1
Consider a relation schema R = (U, V, W, X, Y, Z), on which the following functional dependencies hold:
(U → V, VW → X, Y → W; X → U}
The candidate keys of R are:
1.UY, VY
2.UY, VY, XY
3.UYZ, VYZ, VWZ
4.UYZ, VYZ, XYZ✓ Correct
Solution
The correct answer is UYZ, VYZ, XYZ
Concept:
A candidate key is a column, or set of columns, in a table that can uniquely identify any database record without referring to any other data
Explanation:
The following functional dependencies,
U → V, VW → X, Y → W, X → U
S = (U, V, W, X, Y, Z)
Here YZ is an independent key. So, for every key, the YZ should their. Hence only option 4 is containing YZ for all keys. ∴ Hence the correct answer is UYZ, VYZ, XYZ.
Alternate Method
Options Verify:
UY+=UVWXY,
VY+=UVWXY
Here Z is not closed. Hence option 1 is incorrect.
UY+=UVWXY,
VY+=UVWXY,
XY+=UVWXY Here Z is not closed. Hence option 1 is incorrect.
UYZ+=UVWXYZ, VYZ+=UVWXYZ, VWZ+=UVWXZ
Here Y is not closed for VWZ+. Hence option 1 is incorrect.