Thread: Optimization theory-convex hull help

Can someone help me in going about proving the following?

Let S be any arbitrary set in R^n. Show that conv(S) is the smallest covex set containing S.

I was thinking a proof by contradiction. But am having a hard time getting it.

TIA

Well, if there was a convex superset D of S strictly contained in the convex hull conv(S), then there would be a convex combination of elements of S, contained in D and not contained in conv(S). This contradicts the definition of the convex hull.