3. For the universal relation R(a, b, c, d), consider the decomposition D consisting of R₁(a, b) and R₂(b, c, d), and the set F of functional dependencies { a --> b,c ; b --> a,d ; c --> a,d }.

A. Compute the projection of F on R₁.

B. Compute the projection of F on R₂.

C. Does the decomposition D preserve the set of dependencies F? Give a detailed explanation why or why not. (That is, dont just repeat back the definition of the dependency preservation property, but rather show why the decomposition D either has or does not have this property.)