Provide an appropriate response
-Let int S be the set of all interior points of S, and let cl S be the closure of S (S ∪ the set of all boundary points of S). Which of the following statements are true?
I: If S is convex, then int S is convex.
II: If S is convex, then cl S is convex.
A)II
B)Both I and II
C)Neither I or II
D)I

Question

Quizplus · Accepted Answer

Both statements I and II are true. For a convex set S, both the interior and the closure of S are also convex. The interior is convex because any line segment between two points in the interior remains entirely within the interior. The closure is convex because it includes all the limit points of the convex set, ensuring that any line segment between two points in the closure remains within the closure.

Provide an Appropriate Response