Is the following statement necessarily true about a Boyce-Codd Normal Form decomposition R_1, R_2, \ldots, R_n of R? It is definitely the best possible decomposition for R (based on the information given). (True or False).
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2. Let R be a relation with attributes ABCDE and F={C → D, AC → BDE, AB → CDE, B → CE} (i) (1 point) Find all the keys of R (ii) (4 points) Find a BCNF decomposition of R with lossless join with respect to F. (Show how the decomposition is obtained.) (iii) (2 points) Is the decomposition obtained in (ii) dependency preserving with respect to F? (iv) (5 points) Find a 3NF decomposition of R with lossless join and dependency preserving with respect to F (show the steps). Is the decomposition also in BCNF?
Akash M.
Consider the relation schema R = (N, Y, P, M, C) and assume that the following set of functional dependencies holds on R: F = { N → M, NY → P, M → C} The letters can be interpreted as follows: R = (Model_Number, Year, Price, Manufacturing_Plant, Color). Give a lossless-join decomposition of R into Boyce-Codd normal form. Make sure to use the algorithm and to show all details. Does your decomposition preserve functional dependencies? Justify your answer. Is R in 3NF? Justify your answer. You can use the fact that R has only one candidate key, NY.
Given a relation R(A, B, C, D, E) with functional dependencies: AB -> C and C -> D. a. Find all key(s) of the relation R. b. Which normal form is R in? c. If R is not in BCNF, decompose R, as necessary, into a set of relations that are in BCNF. d. Is your decomposition dependency-preserving? Briefly explain why or why not?
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