functional dependency

Question

GIven a relation instance

X	Y	Z
2	8	4
2	10	6
2	12	6
6	4	4

which of the following FDs  is satisfied by relation

A)XY → Z, Z → Y

B)YZ → X, Y → Z

C)YZ → X, X → Z

D)XZ → Y, Y → X

Answer 1

Z-> Y is not satisfied as when Z = 4, Y has values 8 as well as 4. So, (A) is False.

YZ and Y are unique and hence FDs in (B) are trivially satisfied.

X->Z is not satisfied as when X=2, Z can have 4 as well as 6. So, (C) is false.

XZ -> Y is not satisfied as when XZ = {2,6}, Y can have 10 as well as 12. So, D is false.

Comments

still not understood

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FD says nothing but a relation. A FD X-> Y says that Y must repeat when X repeats. Now, please read the solution and see if you get it.