Solution

The correct answer is A - IV, B - I, C - II, D - III

EXPLANATION:

• BCNF (Boyce-Codd Normal Form):
  • BCNF is a higher version of 3NF (Third Normal Form) in relational database normalization.
  • BCNF is a normalization form that is used when there are multiple candidate keys in a relation.
  • The condition for a table to be in BCNF is that for each functional dependency (X -> Y), X should be a superkey.
  • This "functional dependency is implied by the candidate keys" is exactly what is mentioned in option IV.
• 5NF (Project-Join Normal Form or Fifth Normal Form):
  • This normal form is designed to reduce redundancy in relational databases recording multi-valued facts by isolating semantically related multiple relationships.
  • A table is said to be in the Fifth Normal Form only if it is in 4NF and it cannot be decomposed into any number of smaller tables without loss of data.
  • Here, "every JD (Join Dependency) is implied by the candidate keys" is the definition of 5NF which is option I.
• 1NF (First Normal Form):
  • In this normal form, the data in the table is with no repeating groups i.e., there are no arrays or sets in any of its relations.
  • Each attribute contains only atomic, or indivisible, values, hence the statement "all underlying domains contain scalar values only". So, option II is correct for 1NF.
• 4NF (Fourth Normal Form):
  • A table is in the Fourth Normal Form when it is in the Boyce-Codd Normal Form and there are no multi-valued dependencies about a set of attributes in the table.
  • In this normal form, we ensure that the semantic of storing grouped data is maintained by removing any dependencies of sets of values.
  • This "every MVD (Multivalued Dependency) is implied by the candidate keys" is the definition of 4NF which is option III.

So, the correct arrangements are - A (BCNF) corresponds with IV, B (5NF) corresponds with I, C (1NF) corresponds with II, D (4NF) corresponds with III.