GATE 2024 CS (CS2) – Question 56
A functional dependency $F: X\to Y$ is termed as a useful functional dependency if and only if it satisfies: $X$ is not the empty set, $Y$ is not the empty set, and the intersection of $X$ and $Y$ is the empty set. For a relation $R$ with 4 attributes, the total number of possible useful functional dependencies is ________
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Correct answer: 50
Explanation
Each attribute is in X, in Y, or in neither: 3^4 = 81 assignments. Subtract those with X empty (2^4 = 16) and Y empty (16), adding back both empty (1): 81 − 16 − 16 + 1 = 50.