Question

We now have relational scheme R = {A, B, C, D, E, F, G } and the following
functional dependencies:

• D → AC
• GA → C
• E → A
• GD → BF
• GD → E

And the Following MVDs:

• C→→ A
• F →→ B
• GB →→ C

Asking: Is this relation in the 4NF? Why? If it is not in 4NF, transform it into 4NF.

Answer 1

Fourth normal form (4NF):

Fourth normal form (4NF) is a level of database normalization where there are no non-trivial multivalued dependencies other than a candidate key. It builds on the first three normal forms (1NF, 2NF and 3NF) and the Boyce-Codd Normal Form (BCNF).
It states that, in addition to a database meeting the requirements of BCNF, it must not contain more than one multivalued dependency.

Properties – A relation R is in 4NF if and only if the following conditions are satisfied:

It should be in the Boyce-Codd Normal Form (BCNF). Also, a table should have at-least 3 columns for it to have a multi-valued dependency.

suppose there is a relation R = {A, B, C, D, E, F, G } with functional dependency
set (D → AC). The relational R is decomposed into R1(ABCDEFG) and R2(AD) which is dependency preserving
because FD D → AC is a part of relation R1(ABCDEFG).

Conclusion: - Given relational scheme is in 4NF.