Let R(A, B) be a relation with r > 0 tuples, and let S(B, C) be a relation with s > 0 tuples. We assume that A, B, and C have the same data type. For each of the following Relational Algebra expressions, in terms of r and s, determine the minimum and maximum number of tuples that the result relation can have. In other words, we are interested in the number of tuples the following Relational Algebra expressions can have at least and at most. The numbers have to be given by using the two variables r and s. Please note that you have to give precise and formal explanations for your answers.

a. [4 points] R u rho rum(S)
b. [3 points] (R Da R) pA R
c. [4 points] π4.dRx S)
d. [5 points] ơedR bd S)