The question is :
Find a condition on a metric space$(X,d)$ that ensures that there exist subsets $A$ and $B$ of $X$ with $A \subset B$ such that $diam(A)$ = $diam(B)$.
I know that if $X$ is a metric space and $A$ and $B$ are subsets of $X$ with $A \subset B$ then
$diam(A)$ <= $diam(B)$.
If i assume that the metric $d$ on $X$ is the discrete metric then then diameters of $A$ and $B$ will be the same.
Is this good enough ? or can there be some other condition on the metric space $X$ ?