Question $5$: Normalization $(20$ marks$)$

$($a$)$ Given the schema $xYWZPQ$ and the set $,$

$xYQ,$ consider the decomposition $ZPQ$ and $xYZPQ.$ Is the decomposition

lossless or lossy? Show all work.

$($b$)$ Consider the schema $xYZW$ and a set $F=\{YW,WY,xYZ\}.$ What are

the candidate keys of this relation? Show all work. $($Hint: There are two such

keys; they may or may not be the same as the left$-$hand side of a functional

dependency.$)$

Question $5($continued$)$

$($c$)$ For $($b$)$ on the previous page, is the relation in $3$NF$?$ Is it in BCNF$?$ Explain how

you derived this.

$($d$)$ Consider the relation XYZW and the decomposition $xY$ and $ZW.$ Is this relation

dependency preserving with respect to $F=\{xY,ZW\}?$ Show all work.