From jacobson@math-cs.cns.uni.edu Tue Aug 22 17:12:58 2006
Date: Tue, 22 Aug 2006 12:12:29 -0500 (CDT)
From: Mark Jacobson <jacobson@math-cs.cns.uni.edu>
To: 810-080-02-FALL@uni.edu
Subject: [810-080-02-FALL] Web page is ready...


Hi Discrete Structures students,

      The class web page URL is:

         http://www.cns.uni.edu/~jacobson/c080.html

      and it has links from week #1 to:

         http://www.cns.uni.edu/~jacobson/080/email080classNumeroUnoF2004.txt

      and

         http://www.cns.uni.edu/~jacobson/080/email080Jan13th2004.txt

      which would be very good to review and preview what we will cover
      during the next two or three classes.  -------

      The URL to get to my web page is:

                                http://www.cns.uni.edu/~jacobson

      The 16 week outline it tentative beyond the 2nd week, but I have
      left some of the links to examples and old tests and quizzes up
      on the page so you can see a small portion of the resources that
      will be made available each week on the web page as the class
      proceeds.

      Usually I get the implication operator covered in the first class,
      so we'll do that right away tommorrow.

          if A then B    also written with -------> symbol as  A -----> B

          See if you can understand the TRUTH TABLE for the implies

          A implies B                    A   B   A ----> B
          A ------> B                   --- --- -----------
       if A   then  B                    T   T       T
                                         T   F       F
                                         F   T       ?
                                         F   T       ?

         If A is true Then B is true

         If n is divisible by 4, then n is even          TRUE implication

         If n is an even number, then n is divisible by 4    FALSE

               Why is the 2nd implication FALSE?

               Because there is an instance where:

                    A   B   A ----> B
                   --- --- -----------
                    T   F       F

                  A is TRUE, but B is FALSE, making A ----> B FALSE
                       -              -                       -

         If n is an even number, then n is divisible by 4    FALSE

         Can you come up with an example that proves the statement
         is false?  If you can, you have just done a proof by
         counterexample that:

          (n is even ------> n is divisible by 4)'

           is true, i.e. that

          NOT (n is even ------> n is divisible by 4)
                                                      is true...

      See you tommorrow in class.

      Mark