Answer Happy

Hi. Please help, especially with Part B.
Consider the following interpretation of the terms “point”,
“line”, and “incidence”: • A point is any pair of real numbers (x,
y) such that y > 0. That is, any point in the upper half-plane
of R 2 . [The x-axis (y = 0) is not included.] • A line is either
an open ray emanating from a point on the x-axis and perpendicular
to the x-axis or an open semi circle in the upper half-plane whose
center lies on the x-axis. • Incidence is the usual relation of set
membership. (a) Verify that the above model defines an incidence
geometry (i.e., axioms I.1-I.3 hold). (b) Suppose we change the
model so that we include the x-axis in our allowable points. That
is, points (x, y) satisfy y ≥ 0, and lines are now closed rays or
closed semi circles (they include the end points). How does the
change affect part (a) above? i.e., does this modified model define
an incidence geometry? Fully justify your answer. (c) Does the
modified model in (b) define a Euclidean, elliptic, or hyperbolic
geometry (or none of these)? Fully justify your answer.