Consider the schema R = (A, B, C, D, E, G) and the set F of functional dependencies:AB → CDB → DDE → BDEG → ABAC → DER is not in BCNF for many reasons, one of which arises from the functionaldependency AB → CD. Explain why AB → CD shows that R is not in BCNFand then use the BCNF decomposition algorithm starting with AB → CD togenerate a BCNF decomposition of R. Once that is done, determine whetheryour result is or is not dependency preserving, and explain your reasoning.

Give a lossless, dependency-preserving decomposition into 3NF of schema R of Exercise 7.1.

Consider the relation R = {A, B, C, D, E, F, G, H, I,J} and the set of functional dependencies F = { {A, B} → {C}, {A} → {D, E}, {B} → {F}, {F} →{G, H}, {D} → {I, J} }. (b) Whether (A,B,F} is a super key? Whether {A,B,F} is a candidate key? Why? (c) Whether {A,D} is a super key? Whether {A,D} is a candidate key? Why?

Suppose you are given a database relation R with single-valued atomic attributes (A, B, C, D, E) and a set of functional dependencies F = {AB-C, AC→B, AE, B→D, BC→AE} (a) List all candidate keys for R. (6 points) (b) Name the strongest normal form that holds on R and explain. (4 points) (c) Decompose it into a collection of BCNF relations if it is not in BCNF. Show all steps. (6 points) For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Open Sans,ari... 10pt x² X2 می P> † {;} Ка ? لاک (+ BIUS Paragraph == = 由用 EXE + Œ P - ||| ABC A П "" Ω Ix 用 : 0 WORDS POWERED BY TINY

Consider the relation prereg in the University Database and its transitive closure defined in Section 5.4 of the textbook. Consider the recursive query in Figure 5.16 that outputs this transitive closure. Write a recursive query that finds all direct or indirect prerequisite of BIO-301. Output a table with one column that contains the IDs of all such prerequisites. Note that your query must work correctly not only for the given instance of prereg, but also for all possible instances. Run this query.

Our discussion of lossless decomposition implicitly assumed that attributes on the left-hand side of a functional dependency cannot take on null values. What could go wrong on decomposition, if this property is violated?

Consider the following set F of functional dependencies on the relation schema(A, B, C, D, E, G):A → BCDBC → DEB → DD → A Give a 3NF decomposition of the given schema based on a canonical cover.

Compute the closure of the following set F of functional dependencies for relation schema R = (A, B, C, D, E). A → BC CD → E B → D E → A List the candidate keys for R.

Consider a schema R = {A, B,C, D, E} and the following set of functional dependencies: {AB → C,C → D,D → BE} Is R in Boyce-Codd normal form? Justify your answer.

5 of 40 A decomposition is in 3NF if every decomposed relation is in 3NF. A decomposition is in BCNF if every decomposed relation is in BCNF. Let R(A,B,C,D,E,F,G) be a relation with the FDs: F = {CD → G, DG → C, AD→ G, G –→A, AB → F}. Consider the decomposition of R into R1(C, D, G), R2(A, D, G), R3(A, B, F) and R4(C, E). Which of the following statements is TRUE about this decomposition? Select one: O Ris in BCNF but Not in 3NF. Ris in 3NF but Not in BCNF. R is Not in 3NF and Not in BCNF. O R is in 3NF and in BCNF.