Euclid's Book 1, Choose any two of the following theorems about incidence geometry and prove them in a two-column format. You may assume the incidence axioms I1, I2, and I3, but nothing else. All of them have very similar proofs. Free Book: https://mathcs. clarku. edu/~djoyce/java/elements/bookI/boo kI. html
(a) If l is any line, then there exists at least one point P such that P does not lie on l.

(b) If P is any point, then there are at least two distinct lines l and m such that P lies on both l and m.

(c) If l is any line, then there exist lines m and n such that l, m, and n are distinct and both m and n intersect l.

(d) If P is any point, then there exists at least one line l such that P does not lie on l.

(e) There exist three distinct lines such that no point lies on all three of the lines.