Date: Tue, 13 Jan 2004 13:52:49 -0600 (CST)
   From: Mark Jacobson <jacobson@math-cs.cns.uni.edu>
     To: 810-080-01@uni.edu, 810-080-02@uni.edu
Subject: [810-080-02] Read section 1.1 Pages 1-11

Hi Discrete students,

For the first reading assignment and material we will discover in class,
study over pages 1-11 of section 1.1 of the book.

1.1 Statements, Symbolic Representation, and Tautologies

    A or B       disjunction
    A and B      conjunction
    A implies B  implication (also can be written as:   if A then B  )

                                      (or written as:      A ---> B  )
    not A        negation

    A or (not A)   is called a tautology

    The letters A, B, C, etc. are symbols representing any statement.

    The operations and, or, not, implies are logical connectives.
                   ---  --  ---  -------

    A statement is any sentence that is either TRUE or FALSE.

    Another term for statement is proposition.
                     ---------    -----------

    The truth table for A and B looks like this:

    A   B   A and B                                            A B  A and B
   --- ---  -------    Using 0 for false (zero = F)            - -  -------
    T   T      T         and 1 for true  ( one = T), we have   1 1     1
    T   F      F                                               1 0     0
    F   T      F                                               0 1     0
    F   F      F                                               0 0     0

    TRUE and FALSE are the two possible outcomes for any statement.
    A proposition is either TRUE or FALSE.
    A switch is either ON or OFF.
    A binary digit is either ONE or ZERO.
    A binary digit is either 1 or 0.

    With two light switches there are four possible settings:

    1st          2nd
    switch       switch
     ON            ON
     ON            OFF
     OFF           ON
     OFF           OFF
                                        base 2   base 10
    1st          2nd                    binary   decimal
    switch       switch                 ------   -------
      1            1                      11   =   3
      1            0                      10   =   2
      0            1                      01   =   1
      0            0                      00   =   0

   A B C   A or (B and C)
   - - -   --------------
   T T T     T      T             TTT = 111 = 7         T
   T T F     T      F             TTF = 110 = 6         T
   T F T     T      F             TFT = 101 = 5         T
   T F F     T      F             TFF = 100 = 4         T
   F T T     T      T             FTT = 011 = 3         T
   F T F     F      F             FTF = 010 = 2         F
   F F T     F      F             FFT = 001 = 1         F
   F F F     F      F             FFF = 000 = 7         F
            ---    ---
            ---    1st
            2nd
            and
            final
            result

            Five rows of TRUE and three rows of FALSE.

  We will look at the TRUTH TABLES for AND, OR, NOT, IMPLIES, and
                                   for De Morgan's Laws (page 9)
  during the Wednesday, January 14th class.

  To be emphacized again:  The only prerequisite for discrete structures
                           class is high school algebra.

For the first reading assignment and material we will discover in class,
study over pages 1-11 of section 1.1 of the book.

Please feel free to TOTALLY IGNORE the section titled An Algorithm
                                   on pages 11-13.    ------------

                    Algorithm TAUTOLOGYTEST is most certainly not one
                    of the algorithms we will ever discuss!!!

  Mark