Usually, we're given FDs and we have to find the Normalization level.
Here, we have to derive the FDs and then find the Normalization Level based on it.
For simplicity, I'm renaming the attributes as $A$, $B$, $C$, $D$, $E$
- FDs are derived by schema, not by an instance of the table.
Let's derive FDs by Schema (Requirement Analysis)
Assume that no faculty member within a single department has same name.
$A,B\rightarrow A,B,C,D,E$ (A,B is Candidate Key)
Each faculty member has only one office identified in office
$A \rightarrow C$
So, Not even 2NF.
Option D
Now, let's derive FDs by Relation instance (which is wrong)
$A \rightarrow A,B,C,D,E$
$E \rightarrow A,B,C,D,E$
$C,D\rightarrow A,B,C,D,E$
$C\rightarrow B$ (violates BCNF)
$B,D\rightarrow A,B,C,D,E$
So, 3NF but not BCNF.
Option B
Option B is the official answer, though.