Imagining inside of complement set

Question

I'm undergrad and writing from phone, so feel free to to correct following. I have assignment to show that $( X\setminus A)^{\circ}= (X\setminus \bar A)$, where $A \subset X$.

Is it possible to graphically show left part? As I understand, it is inside of A union with X minus A circumference.

Answer 1

$x \in (X-A)^\circ$ iff there is some open neighbourhood $U$ of $x$ with $U \subseteq X-A$
iff there is some open nhood $U$ of $x$ with $U \cap A =\emptyset$
iff $x \notin \overline{A}$