prove that the sum and difference of two convex sets in R are convex

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- Oct 3rd 2010, 09:20 AMekbioconvex sets
prove that the sum and difference of two convex sets in R are convex

- Oct 3rd 2010, 10:30 AMDinkydoe
Just work from the definitions: If R is convex then for any we have that any convex combination is element of R, with

Now you need to show for 2 convex sets that,

if then is element of

The difference is actually the same excercise...