Consider a relation X $($P$,$ Q$,$ R$,$ S$,$ T$)$ with the FD$$s:

PQ $->$ R

Q $->$ S

ST $->$ P

Q $->$ S is a BCNF violation for X$.$ Suppose we decide

to decompose X into X$1($Q$,$ S$),$ and X$2($P$,$ Q$,$ R$,$ S$,$ T$).$

Which of the following statements are incorrect?

$(1)\{$PQ $->$ R$\}$ is a minimal cover for the FD$$s that

hold in X$2.$

$(2)$ PQ $->$ R is a BCNF violation for X$2.$

$(3)$ X$2$ should be decomposed further into X$3($P$,$ Q$,$ R$)$

and X$4($R$,$ T$)$