Union of Convex Sets Proof

  1. 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}.
  2. jcsd
  3. Dick

    Dick 25,914
    Science Advisor
    Homework Helper

    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?
  4. Thanks so much!
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