Suppose a data cube, \(C\), has \(D\) dimensions, and the base cuboid contains \(k\) distinct tuples.

a. Present a formula to calculate the minimum number of cells that the cube, \(C\), may contain.

b. Present a formula to calculate the maximum number of cells that \(C\) may contain.

c. Answer parts (a) and (b) as if the count in each cube cell must be no less than a threshold, \(v\).

d. Answer parts (a) and (b) as if only closed cells are considered (with the minimum count threshold, \(v)\).