NORMALIZTION

Question

Q.Let R (X, Y, Z, W) be a relational schema with the following functional dependencies:
                                    X→ Y, Y → Z, Z → W and W → Y.
The decomposition of R into (X, Y), (Y, Z), (Y, W) it is asked to find whether it is lossless join and dependency preserving or not ?

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I am sure it is lossless join,but couldn't figure how it is dependency preserving.

Comments

Given dependency is from Y-> Z does this imply Z->Y also, this is what i want to confirm,although Z->Y is one of the possible FD in (YZ) but we haven't provided that in question.

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why you nt taken inderect dependency Z → W and W → Y. = Z → Y

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thanks :)

Answer 1

 All dependency directly mapping to tables except Z-->W

To map this, we need to check whether there is any way to drive Z-->W transitively.

for table YZ , Z-->Y is also there if you do Z+

SimiIarly, for table YW, Y-->W is also there if you do Y+

XY	YZ	YW
X-->Y	Y-->Z	W-->Y
	Z-->Y	Y--W

NOW, Z-->W Can be determine transitively. Hence Dependency preserving