- #1
braindead101
- 162
- 0
Show the following properties of convex hull:
(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
(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