********
*   remember:
    *   no CS 100 lecture this FRIDAY, October 12
    *   that's why HOMEWORK 6's paper is due
        11:00 am on MONDAY, October 15

********
*   ONE MORE EXAMPLE:
    *   If the Green Party loses in the local election, then the 
        developer-friendly politicians will have a majority in the
        city council.

    *   If the developer-friendly politicians have a majority in the
        city council, then the city council will vote down
        restrictions on development on agricultural land.

    *   It is NOT the case that the city council will vote down 
        restrictions on	development on agricultural land OR
        that the Green Party will lose in the local election.

    *   THEREFORE, it is NOT the case that IF the Green Party does 
        NOT lose in the local election, THEN the city council will
        NOT vote down restrictions on development of agricultural 
        land.

    *   IDENTIFY the simple statements in the argument, and give 
        each a letter

        P = the Green Party loses in the local election
        Q = the developer-friendly politicians will have a majority
             in the city council
        R = the city council will vote down
      	    restrictions on development on agricultural land
        
    *   now rewrite the argument in prop logic form:

        P -> Q
        Q -> R
        ~(R v P)

        ∴ ~( ~P -> ~R )

*   make a TRUTH TABLE for this argument,
    and MARK the columns that represent the premise(s)
    and conclusion:

          (*)   (*)         (*)                       (C)
 P  Q  R  P->Q  Q->R  RvP  ~(RvP)  ~P  ~R  ~P->~R  ~(~P->~R)
------------------------------------------------------------
 T  T  T   T     T     T     F     F   F     T        F  
 T  T  F   T     F     T     F     F   T     T        F
 T  F  T   F     T     T     F     F   F     T        F
 T  F  F   F     T     T     F     F   T     T        F
 F  T  T   T     T     T     F     T   F     F        T
 F  T  F   T     F     F     T     T   T     T        F
 F  F  T   T     T     T     F     T   F     F        T
 F  F  F   T     T     F     T     T   T     T        F

    ...and, as shown on document camera,
       when we cross out all the rows where any premise
          is F,
       there is only 1 row left where all 3 premises
          are true,
	  and in THAT the Conclusion is false,
       SO: this argument is NOT valid
       (all of its premises being true does NOT
           guarantee that its conclusion is true)

*   NEXT: a little programming!
    with WeScheme
    (www.wescheme.org)