TrueFalse 1 The negation of Hilberts Euclidean parallel post

True/False

1) The negation of Hilbert\'s Euclidean parallel postulate states that for every line l and every point P no on l there exist at least two lines through P parallel to l

2) It is a theorem in neutral geometry that if lines l and m meet on a given side of a transversal t, then the sum of the degrees of the interior angles on that given side of t is less than 180 degrees

3) Gauss began working on non-Euclidean geometry when we was 15 years old

4) The philosopher Kant taught that our minds could not conceive of any geometry other than Euclidean geometry

5) The first mathematician to publish an account of hyperbolic geometry was Labachevsky

Solution

(a) false (becuase there is only one line parrallel to l)

(b) true

(c) true

(d)true

(e) true