GATE CS 2017 Set 1 — Question 16
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Databases → Normalization → Canonical Cover
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Question
The following functional dependencies hold true for the relational schema :Which of the following is irreducible equivalent for this set of functional dependencies?
Correct answer
(A) V arrow W, V arrow X, Y arrow V, Y arrow Z
Solution
To find the irreducible (canonical) cover, we follow these steps:
In
Current set: .
Final irreducible set: . This matches option (A).
1.Right-hand side decomposition: Split FDs so each has a single attribute on the RHS.
V → WVW → XY → VY → XY → Z
In
VW → X, check if is extraneous. We compute using the other FDs. (using V → W). Since is reachable from via the original set (V → W and VW → X), is extraneous in VW → X. The FD becomes V → X.Current set: .
3.Remove redundant functional dependencies:
Check if Y → X is redundant. Compute without Y → X: (using ). Since is still reachable, Y → X is redundant.Final irreducible set: . This matches option (A).
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