(i) Let X = R2, the two-dimensional plane. Let R(a1,a2):= {(x1, x2) : x1 a1, x2 a2} denote the two-dimensional semi-infinite rectangle with "southwest" corner at the point (a1, a2). Let H consist of all such semi-infinite rectangles, i.e., H = {R(a1,a2) :a1 and a2 are real numbers}. Determine VC-dim(H).

(ii) Generalize the above result to the higher dimensional case where X = Rn,R(a1,a2,...,an):= {(x1, x2, . . . , n) : x1 a1, x2 a2, . . . , xn an}, and H = {R(a1,a2,...,an):a1, a2, . . . , an are real numbers}.