1. Consider the relational schema R(A,B,C,D) and the following set of functional dependencies: S = {A -> B, BC -> A, D -> C}. A functional dependency X->Y (e.g., BD->A) is said to "logically follow" from S if when you compute the closure X+ ({B,D}+ in this case) it contains Y (A in this case). If X->Y does not logically follow from S, then there must be an instance of the relation R which satisfies the dependencies in S, but does not satisfy X->Y. (*Finding this may take a bit of thinking, and working backward.) For each of the functional dependencies X -> Y below show whether it logically follows from S or not. (So if the answer, is "yes", start by computing X+. If the answer is "no", show the appropriate (*smallest) instance.) (i) A -> C (ii) BD -> A (iii) CD -> A (iv) BCD -> A