Consider a relation with schema $R(U,V,W,x,Y)$ and functional dependencies FD given

by:

$UVW$

$Wx$

$xY$

a$.$ What are all candidate keys of the given schema $R?(2$ marks$)$

b$.$ Indicate all the FDs that are BCNF violations for R$.(1$ mark$)$

c$.$ Decompose the relation into collections of relations that are in BCNF$.(2$ marks$)$

d$.$ Determine whether FDs are preserved by the BCNF decomposition. $(1$ mark$)$