I have a set I = {x from R2 : x1<1 v x2>=2}

I have to show it isn't neither open or closed.

Can I do this?:

x1<1then I can choose for that point an open disc of radius r = 1-x1

Every point y in that disc has 2x1−1<y1<1, soy1<1, so every point in the disk satisfies the first inequality so this is open

But if I do the same for x2, then I get 2<y1, so this isn't the same as x2>=2. Can I conclude that it isn't open? I can also say that if x2=2 you cannot say that there is an open ball in I with center z and radius r. So it isn't open.

What have I going to do?