Prove the hamming distance

Question

Response to the following problem:

Prove that the Hamming distance between two sequences of length n, denoted by d_H (x, y), satisfies the following properties:

1. d_H (x, y) = 0 if and only if x = y

d_H(x,y) = d_H(y,x)

d_H(x,z) ≤ d_H(x,y) + d_H(y,z)

These properties show that d_H is a metric.