Interior of a set $A$ is dense in $X$ iff $A$ is dense in $X$ I would like to check if the following statement is true: 

Interior of a set $A$ is dense in $X$ iff $A$ is dense in $X$

It seems to me that they are equivalent, but I couldn't prove or find a counterexample for it.
Thanks!

$\mathbb  Q$ is dense in $\mathbb R$ but interior of $\mathbb Q$ is empty.
