(i)Show that if E is an affine space of dimension man d S is a finite subset of E with n elements, if either ≥ m+3 or n=m+2 and some family of m+1 points of S is affinely dependent, then Shasat least...

(i)Show that if E is an affine space of dimension man d S is a finite subset of E with n elements, if either ≥ m+3 or n=m+2 and some family of m+1 points of S is affinely dependent, then Shasat least two Radon partitions. (ii) Prove the version of Radon’s theorem for cones (Theorem3.6), namely: Given any vector space E of dimension m, for every subset X of E, if cone (X) is appointed cone such that X has at least m+1 non zero vectors, then there is a partition of X in to two none mptyd is joint sub sets X1 and X2 such that the cones cone (X1) and cone (X2) have an one empty intersection not reduced to{0}.

(iii)(Extra Credit) Does the converse of (i)hold?