WEEK 5  
M: Counting subsets of a finite set. Simultaneous induction. 
      3.10. Example. The number of k element subsets of an n element set is "n over k". Proof by simultaneous
                                  induction on k and n.  
               Consequences and connections. (a) The sum of all "n over k" for k \le n.
                                                                         (b) The sum of all "n over k" with alternating signs
              PROBLEMS FOR DISCUSSIONS: Book, p. 82 Exercise 17, 18, 19, 20, 22, 23, 24   
W: The least element principle. Recursive definitions.
      Consequences and connections. (c) the number of even element subsets = the number of odd element subsets
                                                                (d) Explanation why the coeffitients in the binomial formula are combination numbers.
     3.11. Theorem. The least element principle.
     PROBLEMS FOR DISCUSSIONS: No new assignment. Prepare for the midterm.
F: Review.