Question

1. Show that, for any positive integer n, n lines ”in general position” (i.e. no two of

   them are parallel, no three of them pass through the same point) in the plane R2

   divide the plane into exactly n2+n+2 regions. (Hint: Use the fact that an nth line 2

   will cut all n − 1 lines, and thereby create n new regions.)

Answer 1