1. Prove that each of the incidence axioms are independent from the rest.

2. Give a model of incidence geometry in which parallel lines do not exist.

3. Consider the following model of incidence geometry: points are the elements of the set {A, B, C, D, E}, lines are the two element subsets, and incidence is set membership.

(a) Show that for every line and for every point not on that line, there are at least two lines through the point which are parallel to the original line.

(b) In Euclidean geometry, we know that we have transitivity of parallelism. Show by example that this is not the case in this model.