Question

Let $P, Q, R, S$ be relational schemas. Let ``$\rightarrow$'' indicate a functional dependency (FD) in this context. Which of the following best describes the meaning of a functional dependency?

• A. if then or
• B. if then
• C. if then
• D. if and then

Hint:

Always remember: A functional dependency $X \rightarrow Y$ means \textbf{``$X$ uniquely determines $Y$''} or \textbf{``If $X$, then $Y$''}. It is a logical implication, not an AND/OR relationship.

Answer 1

The Correct Option is B

The question asks about the meaning of a functional dependency (FD) in the context of relational schemas in databases. A functional dependency, denoted as \(X \rightarrow Y\), implies a relationship between attributes in a relational database.

Now, let's discuss the meaning of a functional dependency: 

1. If, for any two tuples (rows) in a database table, the values of attributes in \(X\) are the same, then the values of attributes in \(Y\) must also be the same. This formal relationship is essential in ensuring data consistency and is utilized in normal form development during database design.
2. Functional dependencies are a critical part of the normalization process, where they help identify redundant data, such as anomalies that might occur during data updates, insertions, or deletions.
3. For instance, in a relational schema \(R(A, B, C)\), a functional dependency \(A \rightarrow B\) indicates that each value of \(A\) uniquely determines a value of \(B\).

Based on this understanding, the correct answer to the question is:

Correct Answer:

if then

This option correctly conveys the idea of a functional dependency, that the presence of certain values in a table column (attribute) guarantees the presence of corresponding values in another column, thus maintaining the integrity of the relational model.

Answer 2

Step 1: Recall the definition of a functional dependency.
In relational database theory, a functional dependency $X \rightarrow Y$ means:
If two tuples have the same values for attribute set $X$, then they must have the same values for attribute set $Y$.
Step 2: Interpret the logical meaning.
The statement $X \rightarrow Y$ is logically read as:
``If $X$ holds, then $Y$ must hold.''
It does not mean logical conjunction (AND), nor does it involve alternatives (OR).
Step 3: Analyze the options.
(a) if then or: This introduces an unnecessary logical OR. Incorrect.
(b) if then: Correct interpretation of a functional dependency.
(c) if then: Duplicate wording, but option (b) is the standard correct choice.
(d) if and then: Incorrect logical structure; functional dependency is not conjunctive.
Step 4: Conclusion.
A functional dependency in a relational schema is correctly interpreted as: \[ \boxed{\text{if then}} \]