,.,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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,.,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
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}
For the first part, just look at the definition of convex set, and the definition of intersection. What can you do with that?
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.Quote:
Originally Posted by aldrincabrera
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 $\displaystyle A\cup B~?$
