For the universal relation R(w,x,y,z), consider the decomposition D consisting of R₁(w,y,z) and R₂(x,y), and the set F of functional dependencies { y->xz ; yz->w ; x->w }.

Recall that the projection of set of functional dependences G on relation R_x consists of every functional dependency in (G)⁺ that contains only attributes from R_x.

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? Why or why not?