Prove that if a set is nowhere dense iff the complement of the closure of the set is dense. I am able to prove the iff in the forward direction. But, I am having trouble proving the statement in other direction. I am trying to use the definition of dense, but I am not getting anywhere with it.

Assume that complement of (clA) is dense.
Then cl[complement of (clA)] = X.
So complement of (int clA) = X.
Thus int clA is empty.
Hence A is nowhere dense.
