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Let R ( ABCD ) be a relation with functional dependencies { A - > B , C - > D , AD - >

Let R(ABCD) be a relation with functional dependencies {A -> B, C -> D, AD -> C, BC -> A}. Which of the following is a lossless-join decomposition of R into Boyce-Codd Normal Form (BCNF)?
Note: The "lossless-join" property is the generalization of the property discussed in Sect. 3.6.5(p.112), where a test is given to show that the decomposition of a relation into two yields no more tuples when we project onto the relations and then rejoin. The extension to any number of relations is the same: take the projection of the given relation onto each of the relations of the decomposition, and then rejoin (in any order --- it doesn't matter because natural join is commutative and associative). If the resulting join has no more tuples than the original, the join is lossless. In this question, you are really asked to generalize the idea of Sect. 3.6.5. If you have trouble, the choice explanations will give you a hint.
a){AB, AC, AD, BC, BD, CD}
b){AB, AC, BCD}
c){AB, AC, AD, BCD}
d){AC, BD, CD}

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