Generally Normalization is done on the schema itself.
From the relational instance given,we may strike out $FD$ s that do not hold.
e.g. $B$ does not functionally determine $C$(This is true).
But we cannot say that A functionally determines B for the entire relation itself.This is because that , $A->B$ holds for this instance,but in future there might be some tuples added to the instance that may violate $A->B$.
So overall on the relation we cannot conclude that $A->B$,from the relational instance which is just a subset of an entire relation.