Given $D$ is a dense set of a topological space $X$, prove that a set $B$ intersect $D$ if and only if interior of $B$ is not empty. Given $D$ is a dense set of a topological space $X$, prove that a set $B$ intersect $D$ if and only if interior of $B$ is not empty.
The left direction is very easy to prove, however I find it quite hard to show the right direction. Can anyone help?
Thanks!

That is a direct result of the theorem:
D is dense iff for all not empty open U, U $\cap$ D is not empty.  
That theorem follows from the closure of D is the space and
x in $\overline D$ implies for all open nhoods of x, the
nhood intersects with D. 
