1. Verify that Fano's geometry and Young's geometry are both inci- dence geometries. 2. Show that the axioms of incidence geometry are independent. 3. Determine which of the following interpretations of the undefined terms are models of incidence geometry. In any case, indicate which parallel alternative is exhibited by the interpretation. (i) Points are points on a Euclidean plane, and lines are nonde- generate circles in the Euclidean plane. (ii) Points are points on a Euclidean plane, and lines are all those lines on the plane that pass through a given fixed point P. centric circles all having the same fixed center. and lines are the parts of Euclidean lines that intersect the (iii) Points are points on a Euclidean plane, and lines are con- (iv) Points are Euclidean points in the interior of a fixed circle interior of the circle