Question

A relation R is in 3NF if every non-prime attribute of R is:

• A. Partially dependent on the primary key.
• B. Non-transitively dependent on every candidate key.
• C. Functionally dependent on a non-key attribute.
• D. Multi-valued.

Hint:

A famous mnemonic for normalization: "The data must depend on the key [1NF], the whole key [2NF], and nothing but the key [3NF], so help me Codd."

Answer 1

The Correct Option is B

Concept:
The Third Normal Form (3NF) is a standard of database normalization designed to reduce data redundancy and improve data integrity. It builds upon the requirements of 1NF and 2NF.

Step 1: Prerequisites for 3NF.
Before a relation can be in 3NF, it must first be in:
• 1NF: Attributes are atomic.
• 2NF: No partial dependencies (all non-prime attributes depend on the whole of every candidate key).

Step 2: Understanding Transitive Dependency.
A transitive dependency occurs when a non-prime attribute depends on another non-prime attribute, which in turn depends on a candidate key. Formally, if $A \to B$ and $B \to C$ (where $C$ is non-prime and $B$ is not a key), then $A \to C$ is a transitive dependency.

Step 3: The 3NF Rule.
A relation is in 3NF if for every functional dependency $X \to Y$, at least one of the following is true:
• $X \to Y$ is a trivial functional dependency ($Y \subseteq X$).
• $X$ is a superkey.
• $Y$ is a prime attribute (part of a candidate key). This essentially means that non-prime attributes must depend only on the key, and nothing but the key (non-transitively).