GATE CS 2024 Set 2 — Question 56
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Databases → Normalization → Functional Dependencies
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Question
A functional dependency is termed as a useful functional dependency if and only if it satisfies all the following three conditions:
- is not the empty set.
- is not the empty set.
- Intersection of and is the empty set.
Correct answer
50 to 50
Solution
To find the total number of useful functional dependencies for a relation with attributes, we follow the given conditions:
1.
2.
3.
Let the set of attributes be , so . For each attribute , there are three possible assignments in a functional dependency X → Y that satisfies :- and
- Case 1:
- Case 2:
- Case 3: and
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