Question: Consider the following axiom system: Undefined terms: point, line, incident with Defined terms: Two lines are said to be parallel if and only if

Consider the following axiom system: Undefined terms: point, line, incident with Defined

Consider the following axiom system: Undefined terms: point, line, incident with Defined terms: Two lines are said to be parallel if and only if no point incident with both of them. AXIOMS: Axiom 1. Any two distinct points determine a unique line Axiom 2. Any line is incident with at least two points. Axiom3. There is exactly 4 distinct points. Axiom 4. No line incident with all points. Is the following statement independent from this Axiom System? Explain why? i. S: For any line l and any point P not on l, there is at least two lines incident with P and parallel to l Is this axiom system categorical? Explain. Is it a complete axiom system? Explain. ii. iii. iv. Give an example of a non-consistent axiom system, other than the one given in the lecture.

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