# Convex Sets

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• June 23rd 2011, 03:58 PM
aldrincabrera
Convex Sets
,.,How should i do this??

Show that the intersection of two convex sets is convex but the union of convex sets does not have to be convex,.

thnx
• June 23rd 2011, 04:39 PM
TKHunny
Re: Convex Sets
The last part is easy by counter example.

Take x > 0 and y > 0 and

Set 1 {(x,y)|(y/2) + (x/1) <= 1}
Set 2 {(x,y)|(y/1) + (x/2) <= 1}
• June 23rd 2011, 04:56 PM
Ackbeet
Re: Convex Sets
For the first part, just look at the definition of convex set, and the definition of intersection. What can you do with that?
• June 23rd 2011, 05:14 PM
Plato
Re: Convex Sets
Quote:

Originally Posted by aldrincabrera
Show that the intersection of two convex sets is convex but the union of convex sets does not have to be convex,.

If each of $A~\&~B$ is a convex set and $\{p,q\}\subseteq A\cap B$ then the 'line segment" $\overline{pq}$ is in both sets.

On the other hand, if $p\in A\setminus B\text{ and }q\in B\setminus A$ what can you say about $\overline{pq}$ with respect to $A\cup B~?$