Q:

prove or disprove: if $E$ in $\mathbb R$ is a Null set, than its closure is also a null set.

prove or disprove: if $E$ in $\mathbb R$ is a Null set, than its closure is also a null set. 
I think its true. I have no sense of direction on how to start.
Thanks in advance for any response.

A:

Hint: Countable subsets of $\Bbb R$ are null sets. Do you know of a countable subset of $\Bbb R$ whose closure is the whole of $\Bbb R$ (i.e. the subset is dense in $\Bbb R$)?

