Question

A relation $R(A, B, C)$ has the following functional dependencies:
$A \to B, B \to C$
If attribute $A$ is known, the value of $C$ can be determined due to:

• A. Partial dependency
• B. Transitive dependency
• C. Multivalued dependency
• D. Trivial dependency

Hint:

If $A$ is a Primary Key and $B$ is a non-prime attribute that determines another non-prime attribute $C$, the relation violates 3NF because of this transitive link.

Answer 1

The Correct Option is B

Concept:
Functional dependencies (FDs) describe the relationships between columns in a table. Transitivity is one of the fundamental properties of these dependencies, defined in Armstrong's Axioms.

Step 1: Analyzing the Dependency Chain.
We are given two facts:
• $A \to B$: This means $A$ uniquely determines $B$.
• $B \to C$: This means $B$ uniquely determines $C$.

Step 2: Applying Armstrong's Axiom of Transitivity.
The Transitivity Rule states that if $X \to Y$ and $Y \to Z$, then it must follow that $X \to Z$. In our case:
• $X = A, Y = B, Z = C$.
• Because $A$ determines $B$, and $B$ determines $C$, knowing $A$ allows us to find $B$, which then points us directly to $C$.

Step 3: Defining the type of dependency.
This is a Transitive Dependency because $C$ is dependent on $A$ through an intermediate attribute $B$. In database design, this is generally considered undesirable in 3NF as it causes redundancy and update anomalies.