3. Let S be the following statement in the language of incidence geometry: "If l and m are any two distinct lines, then there exists a point P that does not lie either l or m." (a) Show that S cannot be proved from the axioms of incidence geometry. (b) Show that S holds in every projective geometry. (Note: (a) and (b) implies that S is independent of incidence axioms.) (c) Use (b) to show that in any model of finite projective geometry i.e. a projective model with finite number of points, all the lines have the same number of points lying on them. (Hint: Given any two lines l and m, define a function :{l}{m} such that is bijective, which implies that the number of points on l equals the number of points on m.)