Let $C=\{x_2\geq-x_1; x_2\geq x_1; x_2 \leq 3\}$ determine if the set $C$ is convex.
By deffinition a a set $C$ is convex if for all $x_1,x_2\in C$ and $t\in[0,1]$, $$tx_1 + (1-t)x_2 \in C$$
I drew the set and I can tell that is convex. In order to prove that $C$ is convex I just have to follow the definition but I find it difficult to involuve all three equations at the same time. Any suggestions would be great!
Best Answer
Hint: Use that intersections of convex sets are convex. If needed, prove that first.