Problem 12 Consider a relation Book which collects information about book identification numbers "ISBN"), authors, titles, publishers, and years of publication. Hence the relation is: Book (ISBN, Author, Title, Publisher, Year) For convenience, we will henceforth abbreviate these attributes as: Book- (I, A, T, P, Y) Suppose the following set F of functional dependencies are asserted to hold: TP 1 AP T 1 ATP Is the following decomposition of Book lossless? Why or why not? RI(A, T, P), R2(I, P, Y), R3(I, T) a) (4 points) b) Does the decomposition in a preserve all functional dependencies in F+? If so, simply state Yes. If not, give a functional dependency that is not preserved. (4 points) c) Consider replacing F by an alternative set of functional dependencies G: AP IT 1 ATP Is the effect of G the same as the effect of F? In other words, does G+ F+? Why or why not? (4 points)