Assignment 8 (assigned 2/1, due 2/4)

Read section 3.1 and do 1dc,  7 and 8 on pages 89-90.  Follow the proof style used in class for similar proofs (as closely as you can).

Also:  Let f(n) be the number of regions (connected components) formed when n distinct lines are removed from a plane, assuming that no two of the lines are parallet and no three meet in a point.  (This guarantees that the maximum possible number of regions is formed.)  Find f(1), f(2), f(3), and f(4) by drawing lines and counting regions.  Use your experience doing this to guess the recursion formula expressing f(n+1) in terms of f(n).  (Do not attempt to prove your recursion formula or to find an actual formula for f(n) in terms of n.)