,.,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

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- Jun 23rd 2011, 03:58 PMaldrincabreraConvex 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 - Jun 23rd 2011, 04:39 PMTKHunnyRe: 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} - Jun 23rd 2011, 04:56 PMAckbeetRe: 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?

- Jun 23rd 2011, 05:14 PMPlatoRe: Convex Sets
If each of $\displaystyle A~\&~B$ is a convex set and $\displaystyle \{p,q\}\subseteq A\cap B$ then the 'line segment" $\displaystyle \overline{pq}$ is in both sets.

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