When we merge all three tables into one universal relation

𝑅(name, addr, memberno, description, director, serialno, date) R(name, addr, memberno, description, director, serialno, date) and apply the normal-form rules:

It clearly has atomic columns → 1NF holds

There are no partial dependencies on a composite key → 2NF holds

However, it exhibits a transitive dependency

(serialno, date) → memberno →(name, addr) (serialno,date)→memberno→(name,addr) where name and addr depend indirectly on serialno and date, violating 3NF’s “no non-key → non-key” rule

.

Since it fails 3NF, it cannot be in BCNF.

Thus, the highest normal form satisfied is 2NF.

There is a transitive dependency in movies relation, between serial no and Description, hence not in 3NF.

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This is my process of identifying the normal forms:

Tables:
customer(name,addr,MEMBERNO)
movie(DESCRIPTION,director,serialno)
borrow(memberno,DATE,SERIALNO)

Determinants:
memberno -> name,addr
description -> director,serialno
serialno,date -> memberno
serialno -> description
serialno -> director
name,addr -> memberno

CKs:
memberno is CK
description is CK
serialno,date is CK
serialno -> description,director (so serialno is CK)
name,addr is CK

For 2NF, non-prime attributes must be dependent on CK:

movie.director: depends on description (is CK) or serialno (is CK)
borrow.memberno: depends on serialno,date (is CK)

It is in 2NF.

For 3NF, non-prime attributes must be directly dependent on CK, not transitively dependent:

movie.director: depends on serialno, then depends on description (is CK)

It is NOT in 3NF.