Assignment:
Given the metric space (X, p), prove that
a) |p(x, z) - p(y, u)| < p(x, y) + p(z, u) (x, y, z, u is an element of X);
b) |p(x, y) - p(y, z)| < p(x, y) (x, y, z is an element of X).
Provide complete and step by step solution for the question and show calculations and use formulas.