geometric group theory

Problem 1. Let D = Cay(F2; {a, b} ) be the Cayley graph of the free group F2 = (a, b -). For a non-trivial element g E F2, denote by A, the axis of g in T. Let u, v E F2 be two non-trivial conjugate elements. (1) Suppose that Au = Av. Prove that u = v. (2) Find examples of two non-trivial conjugate elements u, v E F2 for each one of the following cases. (a) AunAv = 0; (b) Aun Av = {p}, where p is a vertex; (c) AunAv = [p, q, where p and q are distinct vertices