# Math Help - Convex Sets

1. ## 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

2. ## 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}

3. ## 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?

4. ## Re: Convex Sets

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 $A\cup B~?$