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Each of the proposeod equivalences below on relations r(R) and sS) only holds under (b) ( points) For each equivalence, give a side condition that guarantes the certain conditions. In the equivalences, . X, R and S are sets of attributes, . C is a single attribute, equivalence will hold. The condition should be at the schema level (relation schemes keys, foreign keys) and not at the instance level (number of tuples, specific values). The less restrictive the condition, the better. COUNT(r) returns the number of tuples in r, and 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 ii, X is assumed to be a subset of R.) ii. COUNT s) COUNTr) COUNTS) iv. COUNT(r DA s) COUNT(C)