Prove whether the following tuples are metric spaces or not. (i) (R2, d1), where d1((x1, y1), (x2, y2)) = |x1 x2| |y1 y2|. (ii) (R2, d2), where d2((x1, y1), (x2, y2)) = |x1 x2| |y1 y2|. (iii) (X, d3), where X is a non-empty set and d3 is given by: d(x, y) = 0 if x = y 1 if x = y