GATE Overflow Test Series | Databases | Test 1 | Question: 8

Question

From the following instance of a relation schema $R(A,B,C)$, we can conclude that:(Mark all the appropriate options)
$$\begin{array}{|l|l|l|}\hline \textbf{A} & \textbf{B} & \textbf{C} \\
\hline \text{1} & \text{4} & \text{5} \\
\hline \text{5} & \text{6} & \text{4} \\
\hline \text{1} & \text{3} & \text{5} \\
\hline \text{5} & \text{2} & \text{2} \\
\hline \text{2} & \text{4} & \text{3} \\
\hline \end{array}$$

• A. $A$ does not functionally determine $B$ and $B$ does not functionally determine $C$.
• B. $A$ does not functionally determine $C$ and $B$ does not functionally determine $C$.
• C. $C$ does not functionally determine $B$ and $B$ does not functionally determine $A$.
• D. $C$ functionally determines $A$ and $B$ does not functionally determine $C$.

Comments

Contradicting – https://gateoverflow.in/347493/go-2021-databases-1-15

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mrinmoyh in that question ….question is also asking about instance only

Which of the following functional dependencies are satisfied by the above relational instance 

so no contradiction

Answer 1

Options A, B and C are correct. D is not correct because from a given instance we cannot conclusively say that a Functional Dependency exists though we may be able to conclusively prove that a functional dependency is violated. This is because there can be other instances where the functional dependency is violated. (This is similar to a counter example proving a statement FALSE but an example does not prove a statement TRUE)

So, the correct answer is $A;B;C$

Comments

@gatecse Sir in the question it is asking for the “given instance” so we will make decision based on the given instance of the table but if the word “given instance” was not mentioned then option D should have been wrong right? Can you please clarify once??

This is another similar kind of question where the given instance is considered to check the FD's: Databases: GATE Overflow Test Series | Databases | Test 1 | Question: 15

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Both the questions are asking with respect to a given instance of a relation. But the difference is that one is asking for FDs satisfied by that given instance whereas one is asking for the FD in general for the corresponding relation.

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okay @gatecse Sir got it, very subtle difference actually Thanks.