Mark each of the following statements true or false:
(a) For vectors u, v, and w in Rn, if u + w = v + w, then u = v.
(b) For vectors u, v, and w in Rn, if u ∙ w = v ∙ w, then u = v.
(c) For vectors u, v, and w in R3, if u is orthogonal to v, and v is orthogonal to w, then u is orthogonal to w.
(d) In R3, if a line ℓ is parallel to a plane P, then a direction vector d for ℓ is parallel to a normal vector n for P.
(e) In R3, if a line e is perpendicular to a plane P, then a direction vector d for ℓ is a parallel to a normal vector n for P.
(f) In R3, if two lines are not parallel, then they must intersect in a point.
(g) If v is a binary vector such that v ∙ v = 0, then v = 0.
(h) In Z5, if ab = 0 then either a = 0 or b = 0.
(i) In Z6, if ab = 0 then either a = 0 or b = 0.