eferences Mailings Review Vievw AaBbCe AaBbCDdEe A Norma No

eferences Mailings Review Vievw AaBbCe AaBbCDdEe A Norma No Spacing Heading 1 Heading 2 Heading 3 Question 15 (1 point) True or false? Hilbert\'s parallel postulate states, \"Given that L is any line and P is any point not on L. There exists a line M parallel to L passing through P.\" True False

Solution

Hilbert postulate states that:

Let a be any line and A a point not on it. Then there is at most one line in the plane, determined by a and A, that passes through A and does not intersect a.

So , the number of lines can be 0 or 1, according to Hilbert parallel postulate.

Your statement demands existance of 1 line.

Hence the statement is false

Further , the parallel postulate is valid in euclidean geometry.It would fail in spherical geometry,hyperbolic geometry etc.