Closure of Intersection may not equal Intersection of Closures/Proof 1

Counterexample
Let $\struct {\R, \tau}$ be the real number line under the usual (Euclidean) topology.

Let $\Q$ denote the set of rational numbers.

Let $\R \setminus \Q$ denote the set of irrational numbers.

From Closure of Intersection of Rationals and Irrationals is Empty Set:
 * $\paren {\Q \cap \paren {\R \setminus \Q} }^- = \O$

From Intersection of Closures of Rationals and Irrationals is Reals:
 * $\Q^- \cap \paren {\R \setminus \Q}^- = \R$

The result follows.