1. Given a relational schema, R, prove or disprove the following statements. (a) R is always a superkey for instances r of R. (b) For A E R, if A is a superkey then A is a (minimal) key. (C) Suppose X CR and we have another relation schema S and Y CS such that Y is a foreign key for X. If X is a key (or superkey) for R then Y is also a key (or superkey) for S. (d) Suppose A, B E R and AB is a functional dependency over R. Then AB is a key for R. (e) Suppose X, Y CR are both (minimal) keys for R. Then XnY is also a key for R. (f) Suppose X, Y CR are both (minimal) keys for R. Then XUY is also a key for R