3. Let A, B be non-empty compact subsets of (X, d). The Hausdorff distance is
$d_H(A, B) := \max\{\sup_{a \in A} \inf_{b \in B} d(a, b), \sup_{b \in B} \inf_{a \in A} d(a, b)\}$.
a) Show that $d_H$ is a metric.
b) Let A = [0, 1], B = [3, 5]. Find $d_H(A, B)$ in R.
c) Find $d_H(A, B)$ for the same A, B in R with the post office metric $d(x, y) = |x| + |y|$ for
$x \neq y$, $d(x, x) = 0.$