,.,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
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 $\displaystyle A\cup B~?$