Assignment 5 (English)

1. A lattice point in 3D space is a point with integer coordinates.
   Assume that we have a set of nine lattice points and a line connecting each pair.
   1. Find the number of lines.
   2. Find a formula for the midpoint of the line between two lattice points.
   3. Show that one of midpoints of the lines between the nine lattice points is a lattice point.
2. For each of the following functions, say whether they are injections, surjections or bijections, taking care to prove all your answers.
   1. f: där f(n)=7n+3.
   2. g: där g(n)=n+7.
   3. h: där h(n)=n+7.