## Write first-order formulas over the relational symbols, Mathematics

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Consider the unary relational symbols P and L, and the binary relational symbol On, where P(a) and I(a) encode that a is a point and a (straight) line in the 2-dimensional space, respectively, while On(a,b) encodes that a is a point, b is a line, and o lies on b.

Write first-order formulas over these relational symbols expressing the following (you can use the equality relation between lines/points):

(a) On every line, there lie at least two different points.

(b) Any two lines sharing at least two different points are identical.

(c) For any two different points, there exists exactly one line on which they lie.

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