Points:
A, B, and C.
Lines:
{A, B}, {B, C}, and
{A, C}.
Incidence:
PIl if P is an element of l.
Interpretation # 1
| Points:
|
A, B, and C.
|
|
| Lines:
|
{A, B}, {B, C}, and {A, C}. |
|
| Incidence:
|
PIl if P is an element of l. |
QUESTIONS:
Does this interpretation satisfy the incidence axiom I-1?
Does this interpretation satisfy the incidence axiom I-2?
Does this interpretation satisfy the incidence axiom I-3?
Is this interpretation a model?
Determine whether this interpretation has the elliptic, Euclidean, of hyperbolic parallel property.
ANSWERS:
Does this interpretation satisfy the incidence axiom I-1?
Yes, if P and Q are any of the letters A, B, and C, {P, Q} is the unique line in which they both lie.
Does this interpretation satisfy the incidence axiom I-2?
Yes, every line in this interpretation has exactly two points, therefore at least two.
Does this interpretation satisfy the incidence axiom I-3?
Yes, points A, B, and C are distinct and non-collinear.
Is this interpretation a model?
Yes, all three incidence axioms I-1, I-2, and I-3 are satisfied.
Determine whether this interpretation has the elliptic, Euclidean, of hyperbolic parallel property.
This interpretation has the elliptic parallel property, because any two lines intersect.