This problem from Methods of Real Analysis, 2nd edition, by Richard Goldberg.
For P<x_1,y_1> and Q<x_2, y_2>
define σ(P,Q)=| x_1- x_2 |+|y_1+y_2 |
Show that σ is a metric for the set of ordered pairs of real numbers.
τ(P,Q)=max(| x_1- x_2 |,|y_1+y_2 |)
show that τ defines a metric for the same set .
This document contains two problems on showing that two given functions satisfy the properties of a metric on a given set.