A basis for a set of FD\'s F is any set G of FD\'s whose closure is the same as

Question

A basis for a set of FD's F is any set G of FD's whose closure is the same as the closure of F. That is, exactly the same FD's follow from F as from G. Suppose we have a relation R(A,B,C,D) with FD's A ? B, B ? C, C ? D, and D ? A. Suppose we project R onto attributes ABC. Describe all the bases (consisting of a minimal set of nontrivial FD's) for the set of FD's that hold in ABC. Identify one of these bases from the list below. a) C ? A, C ? B, A ? B, B ? A b) the empty set c) A ? B, B ? A, B ? C d) A ? C, C ? B, B ? A
A basis for a set of FD's F is any set G of FD's whose closure is the same as the closure of F. That is, exactly the same FD's follow from F as from G. Suppose we have a relation R(A,B,C,D) with FD's A ? B, B ? C, C ? D, and D ? A. Suppose we project R onto attributes ABC. Describe all the bases (consisting of a minimal set of nontrivial FD's) for the set of FD's that hold in ABC. Identify one of these bases from the list below.

Explanation / Answer

The answer is D.

Like the original set of FD's , we can derieve the circular relation between these three fds , only via option D.

In other words,

A-> C , C-> B , B->A ..   From the first FD onwards, you can proceed forward to cover the entire ABC .

Hope it Helps :)

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