Incidence Axiom 1 For every pair of distinct points P and Q

Incidence Axiom 1. For every pair of distinct points P and Q there exists ex such that both P and Q lie on e. exactly one line Incidence Axiom 2. For every line e there exist at least two distinct points P and that both P and Q lie on Such Incidence Axiom 3. There exist three points that do not all lie on any one line

Solution

Let P, Q, R be the points, and the lines are PQ, QR, PR and line P.

Clearly P, Q, R do not lie on one line so I-3 is satisfied.

The unique line through P, Q is PQ and similarly there are unique lines through Q and R and through P and R. So I-1 is satisfied.

But I-2 is not satisfied because the line P does not contain 2 distinct points.