Key Candidate key – DBMS

key Candidate key – DBMS

Question 1 UGC NET June-2020
Consider a relational schema S=(U,V,W,X,Y,Z) on which the following functional dependence hold:
{ U → V, VW → X, Y → W, X → U}
Which are the candidate keys among following options?
A – UY, VY
B – UY, VY, XY

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Answer : D
A candidate key is a key through which we can find other attribute uniquely.
Let’s take an example UYZ , to check whether it is candidate key or not, we have to find the closure set of
Attribute UYZ.
Closure set of Attribute: The set of attributes that are functionally dependent on attribute A is called closure set of attribute A. Its is denoted by A+.
(UYZ)+= {U,Y,Z,V,W,X}
Attribute U,Y,Z can be directly found by UYZ itself.
A) (UY)+ = {U, V, W, X, Y} , it is not a candidate key , because we cann’t find all the attribute using it.
(VY)+ = {V, Y, W, X, U}, it is not a candidate key.
B) (UY)+ = not a candidate key.
(VY)+ = not a candidate key.
(XY)+ = {X, Y, U,V, W} , not a candidate key .
C) (UYZ)+= {U,Y,Z,V,W,X} , it is a candidate key.
(VYZ)+ = { V, Y, W, X, U, Z}, it is a candidate key.
(VWZ)+= {V, W,Z, X, U} , it is not candidate key.
D) (UYZ)+= {U, Y, Z, V, W, X} , it is a candidate key.
E) (VYZ)+ = {V, Y, Z, X, U, W}, it is a candidate key.
F) (XYZ)+ = {X, Y, Z, U, W, V}, it is a candidate key.

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