Need help to prove hyperplanes between convex sets

[thelazyman]

Hi,

I need help with this problem.

Prove that a hyperplane H belonging to R^n and its associated half-spaces h^+ and H^- are convex sets.

 

[royhaas]

Use the definition which says that a set is convex if, for each $\displaystyle x, y$ in the set and every $\displaystyle 0 \le t \le 1$, $\displaystyle tx+(1-t)y$ is in the set.