GATE DA 2024 Set 1 — Question 46
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Database Management & Warehousing → Normalization → Functional Dependencies
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Question
Given the relational schema and the set of functional dependencies: Which of the following functional dependencies can be derived from the above set?
Correct answer
(A) VW → YZ; (B) WX → YZ; (D) VW → Y
Solution
To determine which functional dependencies are valid, we compute the closure of the left-hand side (LHS) attributes for each option using the given set of functional dependencies .Option (A):
Compute :
Compute :
From the calculation in (A), .
is not in the closure. Thus,
From the calculation in (A), .
is in the closure. Thus,
VW → YZCompute :
1.Start with .
2.Using
V → X, add . Closure becomes .3.Using
WX → Y, add . Closure becomes .4.Using
Since and are in , WX → Z, add . Closure becomes .VW → YZ is valid.Option (B): WX → YZCompute :
1.Start with .
2.Using
WX → Y, add . Closure becomes .3.Using
Since and are in , WX → Z, add . Closure becomes .WX → YZ is valid.Option (C): VW → UFrom the calculation in (A), .
is not in the closure. Thus,
VW → U is invalid.Option (D): VW → YFrom the calculation in (A), .
is in the closure. Thus,
VW → Y is valid.Therefore, the correct options are (A), (B), and (D).Continue learning with Success Tracker
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