The following functional dependencies hold true for the relational schema R{V, W, X, Y, Z}:V - WVW - XY - VXY - ZQ.Which of the following is irreducible equivalent for this set of functional dependencies?a)b)c)d)Correct answer is option 'A'. Can you explain this answer? - EduRev Computer Science Engineering (CSE) Question

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The following functional dependencies hold true for the relational schema R{V, W, X, Y, Z}:

V -> W
VW -> X
Y -> VX
Y -> Z

Q. Which of the following is irreducible equivalent for this set of functional dependencies?

Correct answer is option 'A'. Can you explain this answer?

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The following functional dependencies hold true for the relational sch...

Given

V -> W
VW -> X
Y -> VX
Y -> Z

We need to find the minimal cover of these FDs
Option B. W->X can not implied by the given FDs, so incorrect
Option C. Y->X can be implied from Y->V and V->X, hence redundant
Option D. W->X can not implied by the given FDs, so incorrect
Option A. Minimal cover of dependencies that can be extracted out as

V -> W
V -> X
Y -> V
Y -> Z

Therefore, option A is most appropriate.

Alternate Solution

Irreducible equivalent functional dependency is minimal cover. Given,

{V → W, VW → X, Y → VX, Y → Z}

W extraneous from VW, since we have V → W,

= {V → W, V → X, Y → VX, Y → Z}

X extraneous from VX, since we have V → X,

= {V → W, V → X, Y → V, Y → Z}

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The following functional dependencies hold true for the relational schema R{V, W, X, Y, Z}:V -> WVW -> XY -> VXY -> ZQ.Which of the following is irreducible equivalent for this set of functional dependencies?a)b)c)d)Correct answer is option 'A'. Can you explain this answer?

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