For a relation R with schema R $($A$,$ B$,$ C$,$ D$),$ let us assume that A is the primary key. And, R consists of the set of functional dependencies F $\{$A $->$ B$,$ A $->$ C$,$ AB $->$ C$,$ C $->$ D$\}.$ Which of the following would violate the $3$NF rule?

AB $->$ C

C $->$ D

A $->$ BCD

$\{$A$\}$