Is the union of convex sets always convex?

[cookiesyum]

Homework Statement

Show that the union of convex sets does not have to be convex.

Homework Equations

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}.

 

[Dick]

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?

 

[cookiesyum]

Thanks so much!