Consider the following statements: (1) We can check if a functional dependency holds by examining a single relation instance. (I) We can check if a functional dependency is violated by examining a single relation instance Only statement IIl is true Only statement I is true Both I and II are true O Neither I nor II is true

This question concerns the logical design of a relation schema LOAN describing the borrowing of a book at a library. If a tuple is in this relation, it means that a specific copy with identifica- tion number catalogNo has been borrowed by a library member with identification number memberNo on dateOut (borrowing day) and has been returned on dateReturn (return day). If the book has not yet been returned dateReturn is null. LOAN (catalogNo, dateOut, memberNo, dateReturn) (a) What would the following functional dependency mean? { dateOut, memberNo} → dateReturn (b) Give all full functional dependencies for schema LOAN, assuming that a book can be borrowed just once per day, that members can borrow many books on any given day, and that members can borrow the same book several times.

Suppose you are given a relation R = (A,B,C,D,E) with the following functional dependencies: {CE -> D,D -> B,C -> A}. Identify the best normal form that R satisfies (1NF, 2NF, 3NF). Explain Why

23 of 40 Let R(A, B, C, D, E, F) be a relation with FD's: {D → CE, C → BDE, E → AD, AF → E, B → DF}. Which of the following statements is correct? Select one: O Ris in BCNF but not in 3NF. O Ris in 3NF but not in BCNF. O Ris not in 3NF and not in BCNF. O R is in 3NF and in BCNF.

For each of the following pairs of expressions, give instances of relations thatshow the expressions are not equivalent. ΠA(r − s) and ΠA(r) − ΠA(s).

Solve the following:

Select all binary relation properties that apply to the following relation: Equal magnitude: |x| = lyl O antisymmetric O reflexive O symmetric O transitive

Give all the keys of R if the functional dependencies on R in each of the following cases

1.A known relationship mode of R (U, F), U= (A, B, C, D, E, G); F={AB->C, D->EG,C->A, BE->C, BC->D, CG->BD, ACD->B, CE->AG}; find the minimum cover of F,then use the Normal Form decomposition algorithm to decompose this mode to 3NF, andcheck if the decomposition has the nonadditive join property.

4