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Sunday, 31 January 2016
Normalization Solved Exercise Set 3
Consider a relation R(A, B, C, D, E) with FD's AB → C, CD → E, C → A, C → D, D → B.
Determine all the keys of relation R. Do not list superkeys that are not a candidate key.
From AB → C and C → D, we obtained AB → D. (as per Transitivity rule)
From AB → C and AB → D, we obtained AB → CD. (as per Union rule)
From AB → CD and CD → E, we obtained AB → E. (as per Transitivity rule)
From above points, we would know that the attributes AB together can identify all the other attributes of R uniquely. Hence, AB is one of the keys.
From C → A and C → B, we obtained C → AB. (as per Union rule)
From AB, we can obtain the rest of the attributes. (See the discussion in Key 1 above). Hence, C is one of the keys.
From D → B, we can get AD → AB. (as per Augmentation rule)
From AB, we can obtain the rest of the attributes. (See the discussion in Key 1 above). Hence AD is one of the keys.
The keys are AB, AD, and C.
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