Given that the attributes of the relation Parts take only atomic values, therefore, the relation is in $1NF$.
From the functional dependency set $F$, there are neither partial dependencies nor transitive dependencies.
Therefore, the relation is in $2NF$ as well as in $3NF$. Now consider the dependency $\text{Partname} \rightarrow \text{SupplierID}$,
which is a non-trivial functional dependency which holds in Parts. Now, from the definition of $BCNF$, Partname should be a
super key in Parts, which is not the case. Therefore, Parts in not in $BCNF$.