Show the following properties of convex hull:(adsbygoogle = window.adsbygoogle || []).push({});

(a) Co(CoA) = Co(A)

(b) Co(AUB) [tex]\supseteq[/tex]Co(A) U Co(B)

(c) If A[tex]\subseteq[/tex]B then Co(AUB)=Co(B)

(d) If A[tex]\subseteq[/tex]B then Co(A)[tex]\subseteq[/tex]Co(B)

The definition of a convex hull is a set of points A is the minimum convex set containing A.

(c) is quite trivial and i can get it.

but i am wondering about (a) and (b) and (d), anyone know if (d) is proven using (b) and (c) or is there another method of doing it.

I am having difficulty explaining (a), I think i understand why they are equal.. it is quite obvious, but i can't explain it well.

and as for (b) i am also lost for words for the explanation

any help would be greatly appreciated

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# Variational methods - properties of convex hull

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