$[4](20\%)$ Consider R$($P$,$ Q$,$ R$,$ S$,$ T$,$ U$)$ with F $=\{$P$->$Q$,$ R$->$S$,$ PQ$->$ST$,$ U$->$RS$,$ UP$->$S$\}($a$)$ What are P$+,$ Q$+,$ R$+,$ S$+,$ T$+,$ U$+?($b$)$ What are the candidate keys? $($c$)$ Show all prime attributes and non$-$prime attributes. $($d$)$ Provide a canonical cover of F$.($e$)$ What is the highest normal form $($up to BCNF$)$ of R$?$ Why? $($f$)$ If R is not in BCNF$,$ provide a lossless FD preserving decompositions of R into BCNF relations?