(i) Given a n affine space (over any field K), prove that there is abijection between affine sub spaces of E and projective sub spaces of ̃E not contained in (ii) Prove that two affine sub spaces...

(i) Given a n affine space

(over any field K), prove that there is abijection between affine sub spaces of E and projective sub spaces of ̃E not contained in

(ii) Prove that two affine sub spaces of E are parallel iff the corresponding projective sub spaces of ̃E have the same intersection with the hyper plane at infinity