Suppose you are given a relation r(a, b, c).

a. Give an example of a situation under which the performance of equality selection queries on attribute a can be greatly affected by how r is clustered.

b. Suppose you also had range selection queries on attribute b. Can you cluster r in such a way that the equality selection queries on r.a and the range selection queries on r.b can both be answered efficiently? Explain your answer.

c. If clustering as above is not possible, suggest how both types of queries can be executed efficiently by choosing appropriate indices.