Provide an appropriate response
-Which of the following statements are true?
I: If $S = \{ ( x , y ) : x - y = 0$ and $x \geq 0 \}$ and if $P$ is its profile, then conv $P = S$.
II: If $S = \{ ( x , y ) : x - y = 0$ and $0 \leq x \leq 5 \}$ and if $P$ is its profile, then conv $P = S$.
A) Neither I or II
B) Both I and II
C) I
D) II

Question

Quizplus · Accepted Answer

Statement II is true because the set $S$ is a line segment from (0,0) to (5,5), which is already convex, so its convex hull is itself. Statement I is false because $S$ is a ray starting from (0,0) extending to infinity, which is not bounded, and thus its convex hull would not be equal to $S$.

Provide an Appropriate Response -Which of the Following Statements Are S={(x,y):x−y=0S = \{ ( x , y ) : x - y = 0S={(x,y):x−y=0

Provide an Appropriate Response
-Which of the Following Statements Are $S = \{ ( x , y ) : x - y = 0$