The problem is : If $(X,d)$ is a metric space with metric $p(x,y) = min(1, d(x,y))$ then prove that any non empty subset of X is bounded
My solution is: $min (1, d(x,y)) < 1$, hence $p(x,y) < 1$. Also $p(x,y) \ge 0$, therefore $0 \le p(x,y) \le 1$. Hence $(X,d)$ is bounded and therefore any subset of X will be bounded.
Request confirm if the logic is correct
