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

Step 1: Understand what a functional dependency means. 
In relational database theory, a functional dependency written as $X \rightarrow Y$ states that:
If two rows in a table have identical values for the attribute set $X$, then they must also have identical values for the attribute set $Y$.

Step 2: Interpret its logical meaning.
The notation $X \rightarrow Y$ is read logically as:
“If X is true, then Y must also be true.”
It does not represent a combination of conditions (AND), nor does it allow alternatives (OR).

Step 3: Examine the given options.
(a) if then or: Incorrect, because functional dependency does not involve an OR condition.
(b) if then: Correct, as this directly matches the logical meaning of a functional dependency.
(c) if then: Although phrased similarly, option (b) is the standard correct interpretation.
(d) if and then: Incorrect, since functional dependency is not based on conjunction.

Step 4: Final conclusion.
The correct interpretation of a functional dependency is:

\[ \boxed{\text{if then}} \]