**Question:**
Check if the following sets are open and/or closed and compute $\operatorname{int}(A) $ and $\bar A$.

a. $A=\{(x,y)\in \Bbb R^2: 0 \le x+y<2\}$

b. $A=\{(x,y)\in \Bbb R^2:x^2+2y^2<1\}$

### What have we tried

Bounding, triangle inequality, Pythagoras theorem. We're having a very hard time proving these formally. Intuitively it's pretty obvious that a is not closed for example. We're supposed to use the method of balls and reductio ad absurdum.