1. The problem statement, all variables and given/known data Show that the union of convex sets does not have to be convex. 2. Relevant equations 3. The attempt at a solution Is it enough to just show a counterexample? Or is that not considered a complete proof? My example is...S = {1} and T = {2}.
Just show your counterexample works. Why is {1}U{2} not convex and why are {1} and {2} convex? Then you are done. Pretty easy, huh?