Let $A$ be a subset of $\Bbb{R}$ such that the following $7$ sets are all different I am suppose to come up with an example of an subset $A$ such that the sets 
$ A$
$int(A)$   
$cl(A)$
$ cl(int(A))$
$ int(cl(A))$ 
$int(cl(int(A)))$
$ cl(int(cl(A)))$
are all different. I am not really sure how to come up with example like that so any hint or idea is great.

Let $A=[0,1]\cup(2,3)\cup([4,5]\cap\mathbb{Q})\cup\{6\}\cup(7,8)\cup(8,9).$ Then note that :


*

*$int(A)=(0,1)\cup(2,3)\cup(7,8)\cup(8,9),$

*$cl(A)=[0,1]\cup[2,3]\cup[4,5]\cup\{6\}\cup[7,9],$

*$cl(int(A))=[0,1]\cup[2,3]\cup[7,9],$

*$int(cl(A))=(0,1)\cup(2,3)\cup(4,5)\cup(7,9),$

*$int(cl(int(A)))=(0,1)\cup(2,3)\cup(7,9),$

*$cl(int(cl(A)))=[0,1]\cup[2,3]\cup[4,5]\cup[7,9].$ 
