Date: Wed, 24 Oct 2001 15:23:07 -0500 (CDT)
   From: Mark Jacobson <jacobson@math-cs.cns.uni.edu>
     To: 810-080-01@uni.edu, 810-080-02@uni.edu
Subject: HW #6 and Monday quiz...

Hi 080 discrete students,

     There is a quiz on Monday.  It will emphacize HW #5 and not have
as much emphasis on HW #6.

     You may turn in solutions to any sets HW #6 problems on Friday that
you got wrong or did not get figured out, if you wish.  I will have the
grader give some extra credit points for that or if you turn in
a problem that was worth 10 points that you got 0 points on, you
will be given something like half credit or so for the improved or correct
version.

     This does NOT apply for the probability question about Pascal,
Fortran and C++ freshmen students from the 300 and it does NOT apply
for the other questions we went over in class such as the
how many students of the 21 students answered only one of the three
quiz questions (the answer was 6).

     We will finish the sets handout on Friday and start in on
chapter 4 on Friday.  The FRIENDS and cross product examples will
be discussed on Friday.  The Cartesian product set of ordered
pairs (x, y) where x and y are both from some set, such as the
Integers or the set {Ross, Rachel, Monica, Phoebe, Joey, Chandler},
allows you to express binary relations, an important future topic
from chapter 5.       ----------------               ------

     Suppose the set A = {2, 3, 4, 8, 9, 18} and we define
     set
         D = { (x,y) | x elementOf A and y elementOf A and x divides y }

     Enumerate or list set D.

     D = { (2,2), (2,4), (2,8), (2,18), (3,3), (3,9), (3,18),
           (4,4), (4,8), (8,8), (9,9), (9,18), (18,18) }

     Why is (3,9) element of set D?   Because 3 element of A and
                                              9 element of A
                                          and 3 divides 9.

     We say D subset of A X A or D subset of A x A,
                where A x A means the cross product
                                   or Cartesian product of set A with
                                                               itself.
     You might want to look at the beginning of chapter 4
and read about inductive proofs before Friday's class.  See especially
the dominos example on page 165 and the computer program code
segments written on pages 169 and 172.

     Mark