GATE CS 2022 Set 1 — Question 31
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Databases → Normalization → Candidate Keys from FDs
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Question
Consider a relation
R(A, B, C, D, E) with the following three functional dependencies.AB → C; BC → D; C → E;The number of superkeys in the relation is _____________.Correct answer
8 to 8
Solution
To find the number of superkeys, we first need to identify the candidate keys of the relation
Using
Using
Using
Since contains all attributes of the relation, is a candidate key.
R(A, B, C, D, E).1.Identify essential attributes: Attributes and do not appear on the right-hand side of any functional dependency. Therefore, and must be part of every candidate key.
2.Check closure of essential attributes:
(starting set)Using
AB → C, Using
C → E, Using
BC → D (since ), Since contains all attributes of the relation, is a candidate key.
3.Check for other candidate keys: Since any candidate key must contain and , and is already a candidate key, no proper subset of can be a candidate key. Thus, is the only candidate key.
4.Calculate the number of superkeys: A superkey is any set of attributes that contains a candidate key. Here, any superkey must contain . The remaining attributes are . The number of ways to choose a subset of these 3 attributes to add to is .
The 8 superkeys are: .Continue learning with Success Tracker
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