(a) Show that the VC dimension of the set of all intervals in Rd, of the form                                    (−∞, x1] ×···× (−∞, xd] (x1,...,xd ∈ R) is d. (b) Show that the VC dimension of the set...

(a) Show that the VC dimension of the set of all intervals in Rd, of the form

                                   (−∞, x1] ×···× (−∞, xd] (x1,...,xd ∈ R)

is d.

(b) Show that the VC dimension of the set of all intervals in Rd, of the form

                                 (x1, y1] ×···× (xd, yd] (x1, y1,...,xd, yd ∈ R),

 is 2 · d.