Consider a relation $(,,,,,,,,)$ and its FD set $=\{,,,,,\}.1)$ Check if $$ in F $+.$ Justify your answer. $(2$ mark$)2)$ List all the candidate keys for $.(2$ marks$)3)$ How many super keys can be found for R$?$ Compute the total number of super keys and list $5$ of them. $(2$ marks$)4)$ Find a minimal cover $$ for $.(2$ marks$)5)$ Determine the highest normal form of $$ with respect to $.$ Justify your answer. $(2$ marks$)6)$ Regarding F$,$ is the decomposition R$1=\{\},$ R$2=\{\},$ R$3=\{\}$ of $$ dependency$-$preserving? Please justify your answer. $(2$ marks$)7)$ Regarding F$,$ is the decomposition R$1=\{\},$ R$2=\{\},$ R$3=\{\}$ of $$ lossless$-$join? Please justify your answer. $(2$ marks$)8)$ Decompose it into a collection of BCNF relations if it is not in BCNF$.$ Make sure your decomposition is lossless$-$joined and briefly justify your answers. $(2$ marks$)$