So I have this one homework assignment where I have to prove the following clause "If $x+y \ge 1$ then $x \ge \frac 12$ or $y \ge \frac 12$". I thought that if I assign $x=y$ and put it like "$2x \ge 1$" and solve the x, does it actually prove that either of them(or both) need to be greater than 1/2?
The clause "If $x + y ≥ 1$ then $x ≥ 1/2$ or $y ≥ 1/2$"
Edit x,y are real numbers
Sorry if this is too simple to post here or something but I've always had problems with the proving assignments which I really need to start learning as I started in university like two weeks ago. I am not asking for complete solution, tips are ok.