Problem 2 Consider a relation R with five attributes ABCDE. For each of the foll

Question

Problem 2 Consider a relation R with five attributes ABCDE. For each of the following instances of R, state whether it violates the functional dependency (FD) BC D. If an instance violates the FD, state two tuples which violate it. In the given instances, digits denote actual attribute values and "a" denotes a variable representing any attribute value. If an instance violates the FD only for certain values of a, state these values. a) (a,2,3,4,5), (2,a,3,5,5)) b) (a,2,3,4,5), (2,a,3,4,5), (a,2,3,6,5)) c) (a,2,3,4,5), (a,2,3,6,5), (a,2,3,6,6), (2,a,3,4,6)3 d) If each of the instances of R listed above is legal, what can we say about the FD (2 points) (2 points) 2 points) AB: it holds, it does not hold or we don't know whether it holds? (2 points)

Explanation / Answer

a) For a = 2,

The following two tuples

(2, 2, 3, 4, 5)       2 3 -> 4

(2, 2, 3, 5, 5)       2 3 -> 5

violate the FD, BC -> D

for the same BC ie (2, 3) we have different D ( 4 and 5 )

b) The following two tuples violate the FD

(a, 2, 3, 4, 5)                 2 3 -> 4

(a, 2, 3, 6, 4)                 2 3 -> 6

c) The following two tuples violate the FD

(a, 2, 3, 4, 5)                 2 3 -> 4

(a, 2, 3, 6, 5)                 2 3 -> 6

d) For the FD, A -> B to be true

A should uniquely identify B for all tuples

There are only two mappings in the above scenario for A -> B

Now for any value of a the attribute A uniquely identifies B. Thus the FD holds true.

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