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Geometry axiom problem?


show that the following system is not a model for axioms I-1 - I-5:

Points: S= {1,2,3,4,5}
Lines: {1,2,3}, {1,4}, {1,5}, {2,4}, {2,5}, {3,4}, {3,5}, {4,5}
Planes: {1,2,3,4}, {1,2,3,5}, {2,3,4,5}, {1,4,5}

Which axiom is not satisfied?

Axiom 1-1: Each two distinct points determine a line.
Axiom 1-2: Three noncollinear oints determine a plane.
Axiom 1-3: If two points lie in a plane, then any line containing those two points lies in that plane.
Axiom 1-4: If two distinct planes meet, their intersection is a line.
Axiom 1-5: Space consists of at least four noncoplanar points, and contains three noncollinear points. Each plane is a set of points of which at least three are noncollinear, and each line is a set of at least two distinct points.

Axiom I-3 is not satisfied. 2 and 3 both lie in the plane {2, 3, 4, 5}, but the line {1, 2, 3} does not lie in that plane.

E = mc2

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