Suppose (Xi , di) are metric spaces (i = 1, 2, ..., n) and that x = (x1, x2, ..., xn) and y = (y1, y2, ..., yn) are points in X = X1 × X2 × ... × Xn. (i). [9 marks] Prove that each of the following functions is a metric on X: ρ1(x, y) = vuutXn i=1 di(xi , yi); ρ2(x, y) = Xn i=1 di(xi , yi); ρ3(x, y) = max{di(xi , yi) : i = 1, 2, ..., n}.