Is the union of convex sets always convex?

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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}.
 
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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?
 
Thanks so much!
 

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