Problem 6 [non-obligatory; 20 bonus points] Let m, n, 1 :1 m P3: of R\" > Rm: Pirl; um] = [221; new: Y = {P3 r I E X} Mark by T the claims in the following list which always [i.e., independently of what are m, n, X satisfying the above assumptions} are true: 1. 2. {:1 2 points] Y is closed, and the set of extreme points of Y is nonempty 2 points] When Y is closed, the set of extreme points of Y is nonempty . :3 points] When X is boundedJ Y is closed, and the set of extreme points of Y is nonemptyr . 3 points] If m is an extreme point of X1 Pm is an extreme point of Y . It} points] If v is an extreme point of Y} then i: = Pm for some extreme point in of X