$($a$)(2\%)$ Define the general definition of $3$NF$,$ which considers all keys of a relation.

$($b$)(6\%)$ Derive the undesirable dependencies when a functional dependency X $$ A violates $3$NF$.$ You need to clearly explain how the undesirable dependencies are derived from X $$ A violating the conditions of $3$NF$.$

$($c$)(4\%)$ How does Boyce$-$Codd Normal Form $($BCNF$)$ differ from $3$NF$?$ Explain why $3$NF adopts a weaker condition than BCNF does.