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Union of Convex Sets Proof

by cookiesyum
Tags: convex, proof, sets, union
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cookiesyum
#1
Sep17-09, 12:45 AM
P: 79
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}.
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Dick
#2
Sep17-09, 12:48 AM
Sci Advisor
HW Helper
Thanks
P: 25,235
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
#3
Sep17-09, 12:51 AM
P: 79
Thanks so much!


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