Only answer number five (it references question four)

4. a. There are several alternative ways to define a distance between two points P1(x1, y) and p2(x2, y2) in the Cartesian plane. In particular, the Manhat- tan distance is defined as dm(P1, P2) = |x1 x2 + ly1 y2l. Prove that dm satisfies the following axioms, which every distance function must satisfy: i. dm(P1, P2) > 0 for any two points P1 and P2, and dm(P1, P2) = 0 if and only if P1 = P2 i. dm(P1, P2) = dm(P2, P1) j. dm(P1, P2)