Provide an appropriate response
-Which of the following statements are true?
I: If $S$ is a nonempty set, then conv $\mathrm { S } \subseteq \mathrm { S }$.
II: If $S$ and $\mathrm { T }$ are convex sets, then $\mathrm { S } \cap \mathrm { T }$ is also convex.
A) I
B) II
C) Both I and II
D) Neither I or II

Question

Quizplus · Accepted Answer

II is true because the intersection of two convex sets is also convex. This follows from the definition of convexity: if any two points in $S \cap T$ are connected by a line segment, that segment lies entirely within both $S$ and $T$, and thus within their intersection, proving the intersection is convex. Statement I is false because the convex hull of a set $S$ (denoted conv $S$) is the smallest convex set containing $S$, which means $S$ can be a subset of conv $S$, but not necessarily the other way around.

Provide an Appropriate Response -Which of the Following Statements Are SSS

Provide an Appropriate Response
-Which of the Following Statements Are $S$