Connected subsets problem

Question

Is it True or False: If $A$ and $C$ are connected subsets of the metric space $X$, and if $A \subset B \subset C$ then $B$ is connected. If true, prove it's true. If false, give a counter-example to prove it's false

My work: I think it's true, right?

edit: false

Answer 1

Let $A:=\{0\}$, $B:=\{0,1\}$ and $C:=[0,1]$ in $\Bbb R$.