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# answer fa f reflexivity c fa given and fa f imply c f

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Unformatted text preview: swer: FA F (reflexivity) C FA (given) and FA F imply C F (transitivity) AB C (given), C F and F E (given) imply AB E (transitivity) Q.9 [20 pts] Consider the relation schema R(A, B, C, D) and the following functional dependencies that hold on R: A BC, B C (a) [5 pts] Find the candidate key(s). (b) [5 pts] Show that R is not in 3NF. (c) [10 pts] Find a lossless-join, dependency-preserving decomposition of R into 3NF. Answer: (a) The only candidate key is AD. (b) For the dependency B C it holds that (i) it is not trivial; (ii) B is not a superkey for R; (iii) C is not contained in a candidate key. This shows that R is not in 3NF. (We could also have used the dependency A A C.) B, or (c) We first construct a canonical cover of the dependencies: {A B, B C}. The algorithm in the textbook results in the decomposition {AB, BC, AD} where AD has to be added since neither AB nor BC contains a candidate key. (If the original dependencies, rather than the canonical cover, is used, the decomposition algorithm would have produce {ABC, AD} where ABC is not in 3NF, due to the dependency B C.)...
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