Consider a relation R(A, B, C, D, E) with FD set S = {A ? BC, CD ? E, B ? D, E ? A}. If R is decomposed into two relations, which of the following is a lossless join decomposition?Select one:a. (ABC), (ADE)b. (ABC), (CDE)c. (ABD), (BCE)d. None of the above
Question
Consider a relation R(A, B, C, D, E) with FD set S = {A ? BC, CD ? E, B ? D, E ? A}. If R is decomposed into two relations, which of the following is a lossless join decomposition?Select one:a. (ABC), (ADE)b. (ABC), (CDE)c. (ABD), (BCE)d. None of the above
Solution
To determine a lossless join decomposition, we need to ensure that the common attribute of the decomposed relations is a key for at least one of the relations.
Let's check each option:
a. (ABC), (ADE) The common attributes are A. But A is not a key for either of the relations, so this is not a lossless join.
b. (ABC), (CDE) The common attributes are C. But C is not a key for either of the relations, so this is not a lossless join.
c. (ABD), (BCE) The common attributes are B. B is a key for the relation (ABD), so this is a lossless join.
Therefore, the answer is c. (ABD), (BCE).
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