Each of the proposed equivalences below on relations r(R) and s(S) only holds under certain conditions. In the equivalences, . X, R and S are sets of attributes, C is a single attribute, COUNT(r) returns the number of tuples in r, and D d is natural join. (a) (4 points each) For each equivalence, give example schemas and instances for r and s where the equivalence does not hold. (Assume that the expressions contain no syntax errors. For example, in i, X is assumed to be a subset of R.)